They are making an argument against keeping their wallet software open source. I am not sure if I agree with their argument, and I know that other wallet software has had similar problems with malicious clones. Electrum is one example. Unlike electrum, I understand that Trust Wallet is a mobile wallet, that must be downloaded via an app store. It is much more difficult for someone to find the "correct" version of an app on the iTunes/google app store than it is to find the correct/official website for bitcoin core or for electrum.
They outright lie on their website when they claim to be open source. If being closed source isn't enough to convince you to stay away, then them outright lying to you should be. They are also owned and operated by Binance, so you can guarantee you will have absolutely zero privacy when using Trust wallet.
Avoid it.
The fact that binance manages the wallet software certainly gives me pause. However, I think that the "open source" claim is being confused. I don't see the claim on the download page in either the iTunes nor google play app stores. I do however see that people can "submit" DApp's that can run "on top of" Trust wallet.