But you dont hourbuild w an instructor unless you want to...
This is not always the case. Many schools will require you to take an instructor as part of its insurance requirements to fly a twin. Sometimes its not only for an initial checkride either but until you have hit a predetermined min number of twin hours. Other schools like Ariben go down the safety pilot route.
In anycase the whole point of this thread wasn't to discuss what an FAA pilot can or can't log it was to advise JAA hour builders that they need to tread carefully when going to the US for twin time as invariably they will only be able to log half the time that they pay for. It may well be the case that the "deals" on offer are still competitive but the maths needs to be done in the first place and we don't want some poor punter incorrectly logging time and being pulled up for it at a later date or worse getting his hard earned licence revoked.