is "not your keys, not your coins" excessively dramatic?

only talking about binance. not other centralized exchanges. i have plenty of top coins in my binance account that i plan on holding long term. From researching for the best wallet that will support all your coins, managing all of them , to securing your wallets is kinda stressful. haha been using binance for years now and i had no issues at all, but my portfolio has gotten chunkier now compared to when i started and i want it more secured. anyway, trust wallet seem to be acquired by binance, does it mean all coins from binance are actually supported? is binance wallet same as trust wallet?