Additionally, the input address isn't actually gotten from any public key in the input. Rather that address is retrieved by checking the specified output since there are special p2sh addresses that exist that don't even use public keys anywhere in them.
It is possible to determine the addresses based on the pubkeys or redeem scripts when those appear in input scripts, without having to check the transaction that is being spent.
Maybe I'm using the wrong terminology here, but I can show you an example if you want.