Can the relay servers, when used as fallback, read the data between two parties by providing its own public key to both of the peers?
So the relay is never in a position to send you the wrong public key, because it doesn’t give it to you in the first place.
Only the owner of the corresponding private key can initiate a connection from their public key, or receive a connection attempt to their public key.
Let's say you have alice and bob talking via a relay. Even if you have the private key of alice, you can impersonate alice to bob, but not vice versa. So you can't initiate a connection between the two.
To really intercept data you would need the private keys of both participants.