No, I think you are correct. There appears to be no additional burden over maintenance done in compliance with FAA regulations - if you are privately operated SE or ME piston, or SE turboprop.
This is much better than rumours circulating for the past few years, which amounted to the FAA maintenance having to be anything from supervised to duplicated by an EASA CAMO, which would have been a huge waste of money and probably unworkable since an EASA MO has to authority under ICAO to sign a release to service for a non EASA machine, and if you cannot sign a RTS then everything you do is legally meaningless.
King Air owners are not going to be pleased though.
For commercial use, the provisions are onerous but ISTM this is barely material since commercial use of foreign regs has never really been possible, outside the AOC environment.
EASA licensing proposals however still remain, which is that EASA licenses will need to duplicate the FAA ones (i.e. every FAA PPL/IR will have to get himself an EASA PPL/IR, and EASA is not proposing any conversion options whatever). However, bizzarely, when this came up in the bizjet forum (I posted it there) nobody thought this was real, and other people I know think the document is being misread...