The clue was that the first time Data said that they had been unconscious for 30 seconds, and then they found things like Worf's healed injury which showed otherwise. That evidence would still be there (if Crusher could remove all evidence, why didn't she do it the first time?), so they're going to find it again.
The thing with this one is you have to accept that the characters aren't trying to remove all evidence of the reality of the event, because yes, that is virtualy impossible. There will always be things that can be traced to the truth. Any tampering Data & Geordi do to the ship's systems, they can certainly figure out they did, if they look deep enough
The same is true of Crusher's medical data. If she can measure our biological clocks at a physiological level, there is no hiding that reality entirely. The truth is out there if they go looking for it. The intent behind their hairbrained solution is to fool themselves enough to NOT go looking into it.
They are merely trying to minimize the evidence of it, so they don't get their curiosities up. If Bev never sees her plant growth, does she begin her campaign to investigate? Does Worf then ever admit he has some wrist discomfort, if he's not ordered to report such things? Without that contrary evidence piling up, do they begin doubting Data, & really comb through everything with dogged intent? Maybe not. They just want to stop the
1st dominoes from falling. Bev's plants, Troi's whackadoo side effects, Data being a shitty liar lol. After dealing with that they maybe don't bother questioning the cover story. That's their half-assed hope at least
I still think it would be safer if they did all that cover story nonsense to placate the Paxans, & then just had Data confess it all at a safe distance, so to be sure that cover story never has a chance to get debunked... Ever by anyone who thinks to ask.