There are far less cynical ways to look at these events:

• First off, you could assume that Blackburn has always had these views of pro business rights. ISPs aren't giving her money to influence her, they are giving her money to make sure she gets elected instead of someone more pro-privacy. Similar to how anyone in this thread who has ever given money to a candidate can probably attest: The money wasn't to influence the candidate, but instead was to help make sure the candidate they liked won. The only difference is the candidate business like tend to be the candidates that best serve their own interests.
• Secondly, you could assume that Blackburn did change her opinion but based on information presented to her by lobbyists. It is lobbyists jobs to convince politicians of the benefit of passing positive bills for their clients and some of them are very good at doing just that.

Realistically, it is all three effects. Selecting politicians already leaning towards your platform, convincing them through information to lean further, and giving their campaign money to help persuade them more. But you should note that the money given can only be used for campaigning and isn't even the same as a bribe even in the worst case scenario.