I hear your frustration. I've been told by my contact in the Consumer Affairs office of USPS, that there had been a memo circulated around the end of December saying that the envelopes could be no more than 3/4" thick. And of course, you are correct in noting that there is no maximum thickness mentioned on the USPS website, at least not as part of the definitions of the flat-rate envelope service. Or anywhere along the path one would take to purchase postage for such an envelope.
However, there is a publication on www.usps.com - I think it's called the Consumer's Guide to Mailing - where it does specify a 3/4" thickness, though it does not really specify what kind of envelopes or what class of mail service it pertains to.
So the confusion will continue. However, I have not had a report of an envelope being delivered postage due in a couple of weeks now.
And yes I just knocked on a wooden chair to be safe!