There aren't really any other tools browsers can use for this right now. The process of logging in looks like basically: you type your password in google, google gives you back a cookie, your browser makes a request with that cookie and the server knows who it's for.
The browser doesn't have access to the MAC. Google *could* (and probably is) checking the IP address, but it's all heuristics because your IP address may change at any time, e.g. cell phones have very unstable IPs, hop in a plane and land with an IP from another country, etc.