1. They give you custodial wallets
You only have your public address to receive your cryptocurrency. You don't have private key, seeds (depends on different cryptocurrency)
2. They give you non-custodial wallets: you have private keys or seeds.
You have control on your crypto but not completed control. They can have data for your identities, emails and some security protections as confirmation for new suspicious log-in, etc.
If you lose access to your email, your 2FA and don't know how to recover your wallet with other softwares, you lose your crypto.
They can (or can not) support users to recover cryptocurrency but you can not blame on them or create any scam accusation on them.