You are right.
First time I see this wallet and I mixed it up with Rabby wallet from rabby.io, that is not supporting bitcoin.
I will have to do more testing to see how it works, but I wish they had version that could be downloaded and installed, not only web version.
It is easier to attack web wallets and scam users with fake phishing websites.
Another thing I noticed, Rabbit wallet only support Bitcoin, ethereum and another shitcoin.

As for their swap feature, this is done by using third-party services and exchanges.
I would first read the terms before doing any swaps there:
https://rabbit.io/docs/legal/swap-terms-of-use.html
https://rabbit.io/docs/legal/swap-privacy-policy.html