^I get what you're saying, but in this case I don't think it's quite right. Transporters have to run on the quantum level resolution for organic beings to survive a transport. Quantum is the smallest you can go in this scale, so basically it is like reassembling that LEGO castle one piece at a time. It's tedious and it takes a lot of data storage, but apparently it's not a problem for those FTL computers of the 24th century. If transporters were to "cheat" as you say, then they would have to be scanning on a lower resolution, like atomic or molecular. That would allow them to break apart matter in bigger chunks, and therefore require less data storage to reassemble them, but it would probably be detrimental to an organic being.
"Second Chances" also seems to confirm that raw matter/energy can be used to recreate an object from the transporter data. It's not as if Thomas and William Riker were created from the same lump of matter that was the original person. The second containment beam must've contained an amount of raw material from the Potemkin.