Is it safe to store crypto on non-native chains?

I know we shouldn't let our crypto on exchanges, but the transfer fees for some of them were quite high.

So I got them to my wallet using base, bnb, and polygon chains.

However, I didn't know until a while back that these crypto that I now have are only pegged tokens, not the real assets.

On top of that, a little research showed me that binance chain uses a mechanism whereby your validation power is proportional to your staked bnb.

Would that mean that Binance can fake transactions if they have more than 50% staked bnb?

Did I get anything wrong and should I bridge my crypto back to their native chains?