When you call the OTC desk and wire them dollars they mint stablecoins using their account with - presumably - Bitfinex. Bitfinex issues Tethers no different than Coinbase/Circle issues USDC in a just in time transaction.
You either receive the Tether you asked for to make your own trades, or they keep the Tether and purchase the crypto you really wanted. In either scenario, someone besides the OTC has the Tether now.
There is no reason to use custodial exchanges for your fiat onramps. They put you at a major disadvantage in speed.
It is strange that this is to be the smoking gun for people against Tether. These kind of juvenile inexperienced arguments (seen in other comments) are why more serious scrutiny of Tether takes so long, because its mixed up with all this benign stuff put in front of regulators who have a huge learning curve already.