Lobbying is very different from vote buying. Vote buying is saying to someone, "I'll buy your vote for $X". If votes are anonymous, then there's no way to verify that you actually got what you paid for.
Presumably there are reliable votes on either side that are well known : subtract those from the result and you may have a fair idea whther your puppet obeyed his master. It might not be easy to confidently disobey.
Votes by people in elections are what’s being contemplated as being bought, not votes by a much smaller group of representatives on specific legislation.