I never said Binance holds 1 USD (cash) per BUSD. I said that at the moment you can redeem 1 BUSD for 1 USD without any issues. BUSD is backed by both cash and US treasuries. Do they have enough liquidity if every single BUSD wants to be claimed? Probably not on the same day, but in a short time span, yes. Note that BUSD was approved by NYSDFS, which should︀ say a lot considering barely any stablecoin has been approved anywhere in the US.
In the case of USDT, Tether had $20B worth of withdrawals in less than two months︁ and they were able to fulfill them. It is true that they do hold some︂ more risky assets, but they've said that for example, commercial paper has been reduced significantly︃ and they're looking to get completely rid of it. They're being audited by a non-offshore︄ accountant firm too, you can check the reports.
But before making this any longer, the︅ only point I was making is that the peg has nothing to do with the︆ liquidity of a pair in an exchange as you were saying. Maybe in one exchange︇ 1 BUSD buys you $0.9 worth of BTC, but that doesn't mean BUSD is worth︈ $0.9 as you can redeem it for $1. Just trying to explain you what peg︉ means here.