Unproven maybe, but very strongly implied, and Tether have done nothing to try to prove the claims incorrect.

There have been a number of shady activities which strongly suggest that Tether do not have the USD backing that they claim. They released a very vaguely worded letter from an unknown bank residing in a tax haven saying they have a "portfolio cash value" equal to USDT. Portfolio cash value means any asset when sold for cash. They also quietly dropped the 1 USDT = 1 USD statement from their terms and conditions, and replaced it with a similarly vague statement about being backed up by a variety of assets. They could print 100 million USDT from thin air, use it to buy bitcoin, and then claim the USDT is fully backed up.

They could quite simply submit to a full audit any time they like (or at any point over the last 18 months since these allegations started), and the whole thing would immediately be done with. The only reason they have for continuing to refuse an audit is if they have something to hide.