Usually, such references are completely erroneous or subject to interpretation. One would have to go to each episode to see what is said or shown.
In this particular case, let's see what each episode has to say.
"Lonely Among Us": The word "replicator" is never even used. The tidbit being referred to is apparently this phrase: "You've seen something as fresh and tasty as meat, but inorganically materialised out of patterns used by our transporters." This neither supports or contradicts either of the models of replication: matter out of energy, or matter out of other matter.
"Hard Time": All we get wrt the replicator is that one puts the dishes back into it after eating. We saw such things in "Cardassians" already; why this particular episode is picked as a reference is unknown. Again, no real support or objection to the first claim made in the article. Only the second claim about recycling is supported.
"The Ascent": Again a reference to putting dishes back into the machine, only relevant to the second claim.
"Year of Hell": No idea what MA wants to reference here, as the replicators go offline for most of the episode.
"Memorial": Another reference to putting dishes back into the replicator.
So basically all that these supposed references give us is that dishes should be put back into the machine or mommy gets angry. We don't even learn what happens to the dishes when the button is pressed. Are they really recycled, or merely destroyed for convenience?
The first claim made in the entry is baseless in light of these particular references.