Most lightweight Bitcoin wallets connect to random servers controlled by only-God-knows-whom and send your wallet addresses to them in order to calculate your wallet balance. Those servers can collect your addresses, lie about the amounts that those addresses have, and do all kinds of things. Given that those servers are offered for free to you, even when they have hosting and maintenance costs, it is reasonable to assume that you are the product.

Wasabi, on the other hand, doesn't use that model. Wasabi allows you to select the server that you want to connect to and it doesn't share any information with the selected server. Instead, it requests compact filters which are the same for everybody. Given that Wasabi connects to the selected server using Tor by default and that all clients make the same requests to the server, there is no way a server can identify you and send anything different to you.

In summary, it is exactly the opposite of what Bitcoin.org says. Wasabi is designed to be private while the rest are, in general, not. And that means that Wasabi doesn't send your info to servers as the others do, which reduces the chances of any server lying to you.