The claim on their website is clearly lying. But that's not the case on their GitHub repository page since "Trust Wallet Core" is not "Trust Wallet".
Sure, but they rely heavily on the fact that most users (and probably almost all users who are using a closed source wallet owned by Binance) will be unaware of the difference between a library being open source and the app being open source. Lots of similar statements on their Twitter account not clearly making the distinction, such as:
https://nitter.it/TrustWallet/status/1271248054755229697#mhttps://nitter.it/TrustWallet/status/1104686959304368128#mThey also lie about it on Binance:
Moreover, the wallet’s code is open-source, which means that the code has been thoroughly vetted by developers across the globe.
A community-driven, completely open-source, multi-coin crypto wallet.
Trust Wallet (trustwallet.com) is a self-custodial wallet that is secure, open source and decentralized.