I think I've actually sold some usdt to binance vendors on the first page and never have I experienced such.
From what I know, when ever you want to use the p2p exchange on binance or any other exchange, make sure you are trading in stables, this means that, you will have to first of all sell your bitcoin for usdt in the exchange spot market, then trade usdt with vendor for local currency through the exchange's p2p market.
I will tell you why...
There are many scammers in Nigeria, using stylish ways to scam traders off their money, no matter how small, when you are trading coins that are unstable in price, like bitcoin, Ethereum, and so on, in the p2p market, there is a very high chance you will come across vendors who will use the instability in the price of bitcoin to send you lesser amount of money than what is supposed to be the agreed amount, they will give excuses like "in the process of the trade, the price of bitcoin dropped a bit, which also have affected/reduced slightly; how much they were willing or going to pay you for your bitcoin".
So, to avoid coming across such, I always first of all exchange my bitcoin for a stable coin (mostly usdt) in the spot market, before I proceed to the p2p market to trade the usdt for my local currency.