But we know that's not how transporters work. If that was the case you wouldn't be able to get "accidents" where you end up with two copies of the same guy. The transporter must work like the replicator, not the other way around.
Also, that doesn't work with some of the stuff they say, like how they don't replicate anything alive, and so food does taste noticeably different. Plus... you know, no massive farm deck anywhere on the Enterprise and no transwarp to beam that in from a planet, so... we're going to have to accept this stuff may be just handwavy bulls#!t at some point.