You said half of correct information, but a non-custodial wallet must be open source and well-reviewed so that you review it yourself or ensure that at least several developers read every line, or at least most of the lines.
Closed-source wallets can claim to be safe, but the number of people who have reviewed the code is very limited, and it could be that one of the previous developers in the wallet found a bug and decided to exploit it in the future, this if you trust the developer team.


This is the argument that they defend themselves if you lose your money, which is that they do not have access to the private key, and therefore you bear all the risks.

Avoid it.