It doesn't stop being true because it was never true. K was grasping for purpose and meaning to his life. That is why all of his energy outside work went to Joi, who could never truly offer it. He finally found it in one implanted memory and the right circumstances to make him consider for even a moment he might be more than the soulless automaton he assumed himself to be, that he had been programmed to accept as his default state. Those moments or hours or days of hope and possibility allowed him the "soul" he had assumed was impossible for him to possess.
Have you never thought for one moment that maybe you could reach out to the remote control and bring it to your hand? That one day a letter might come to you and reveal your secret lineage? Your acceptance to Hogwarts or the secret last will from a grandparent who kept their true nature secret? That you would awake one morning to find out you have a destiny and a purpose beyond the everyday doldrums of mere existence?
K's belief that he could be that child was nothing more than that. He ignored the inconvenient truths momentarily to allow for that quantum of possibility. Of hope. It was implanted in his mind, as real as any other memory, so one can presume it wasn't that hard.
It was true in the story, until the reveal (and as I am arguing, in one evidence based interpretation, is still true after) because that’s how it works. Once K no longer thinks he is just a replicant, nor do we, the audience. A replicants childhood etc memories are a constructed narrative (like Rachael’s, which were borrowed of course, as they didn’t use the memory making tech we see here, and copying memory wasn’t illegal.) as otherwise they wouldn’t work. Yes they know they are false, but as it’s part of their system, they still make sense. That orphanage memory is revealed to be true, meaning anything else he remembers directly related to it is also revealed to him as true. He can doubt some of it...after all, we know memory implants are not just made for replicants, Stelline is a freelancer, Wallace is one of her contracts, but only Wallace makes replicants. Who are the other memories for?
You can’t, as she says, just bung a bunch of unrelated stuff in there.
Every Replicant, therefore, has a memory of a life, they just know it’s not real because they are replicants and are programmed to obey. This is explicit. It’s one of the ideas the film explores...replicants at this point are replicants because they believe they are, because they are told they are. ‘How can it not know what it is?’ Well...now they do, that way they don’t go nuts and kill people, they know their place. (Soulless..ties into the race arguments too, historically part of dehumanising groups involved regarding them as being born without souls.) It’s a disturbing idea (one used before in wider BladeRunner media) but basically it’s very easy to make a human believe it’s a replicant (Wallace tries sewing that idea into Deckard in this film, because of the existing conflicts in the first film...and the deleted ‘made for each other’ ending.) you just bung a memory in there, of learning everything prior to say last year is false, tell them they are a replicant and off they go. If this wasn’t possible (because of super strength etc....) you wouldn’t need VK tests or eyeball serial codes (again, easily faked, Chew makes eyes in his shop...they aren’t all for replicants, he wouldn’t need a shop, and wouldn’t advertise...replicants are illegal on earth.) you could just arm wrestle or ask someone to open a really impossible jar of pickles to discover them.
So, it has to be believable, or there’s no surprise in Freysa’s ‘revelation’. Except, after this, they continue making sure that each time it is discussed, it is done so in a way that still gives it possibility. The other possibility it opens is the ‘twins’ likelihood, which explains and is supported by stuff appearing throughout, and particularly the ending scenes. Everything that supports Stelline being the child, has to support K being the child also, but...it carries on doing that even after he ‘knows’ he isn’t the child.
That’s how you do things writing a detective story anyway (k is a detective, he follows the evidence, and visibly does NOT want to believe he is the child, until it’s inescapable. There’s the horse in his pocket, found because of a memory we know ‘someone lived it’ and there’s Freysas word on the other...except, all the other evidence says there were two children, and Freysa never ever says that other evidence is wrong. Stelline never says the memory is implanted, never says it’s her memory. All we know for sure is, it happened.) you make sure your evidence supports as many possibilities as possible, until the detective figures it out and finds the evidence that narrows it to one....K actually never receives that evidence, it just narrows the ‘suspects’ to two...him and Stelline, because Freysa clearly knows Stelline is the child she dressed in blue.
Now..ignoring the hole in ‘how do you prove this kids mother was a replicant?’ and assuming you can somehow do this, a female is far more useful to prove the miracle of conception...here is a replicant (since Stelline must somehow show as one for Freysas plan to even work.) and she is pregnant (look at her bump! Bet it’s a boy, it hangs low, let’s all start knitting....) is a visible miracle. Here is a replicant and a pregnant woman he got pregnant! Is just too easy to doubt, unless you are distributing porn of the conception.
The child or children are actually essentially useless to Freysa anyway...having one pregnant replicant doesn’t mean they are all suddenly gonna be able to have kids and define themselves fully as a race, it’s literally just the symbol she’s after. And she had that, but she died. Wallace is the only one who can glean anything, who can make them able to reproduce, but he’s an asshole. It’s about control with both of them. (If you like you can call it the means of production.)
If hiding K in the LAPD makes no sense, then nor does having Stelline work as a contractor for Wallace. This actually makes Mariette into the only other likely candidate for being the child...she’s off radar, describes herself as a real girl in a roundabout way, is mostly under the protection of Freysa, and is the only other person who pays attention to the horse. But...it’s from the tree.
Literally the only contradiction is the ‘long hair = girls, shaved head =boys’ in the memory, but I am not sure that holds when we see the orphanage, and no-one remembering that memory is gonna know what the back of their own head looks like anyway. We watch the memory.)
Finally, Deckard can’t help falling in love with K...the song is playing XD
All the best memories are hers....(he hates his memories of being a Blade Runner, or losing Joi etc...he already had to suicide set up shot under the Joi hologram, K wants death at that point, so sadly, but wants it to mean something. This is true for either reading...he believes Stelline deserves happiness, and Deckard too, they are both Blade Runners Who rebelled and lost their wife. Widowers.)