That's actually not true. Keeping their job depends on winning elections, and their staff absolutely keeps track of who from their constituency calls or contacts their office and expresses a particular opinion on a particular issue. Because if someone cares enough to call, they definitely care enough to vote, and if one issue gets a ton of call-ins it's a strong indication to them about how people are going to vote about that particular issue.
It's not the whole story; legalized bribery has a lot to do with how they make their decisions also. But saying they completely ignore people calling in and telling them how they feel about particular issues is ridiculous.
Here's a citation for it. I don't know if you want to listen to that person any more than you want to listen to me, but it's accurate.