There is a good chance you are right. With that said, privacy isn't important to Google and Facebook, but net neutrality is important to their business. I think if net neutrality repeal were in a congressional bill, a lot of big companies would come out to lobby against the repeal. That has a chance of making a difference, whereas in this case everything is up to Ajit Pai.

Also, if it didn't make a difference if you used a bill or not, why wouldn't the conservative FCC commissioners just strike down the privacy rules at the FCC and be done with it? My guess is because they want to make it harder to bring privacy rules back if a democrat president were elected.