So, if the House Republicans aren't in the pockets of the insurance companies, then why did they attempt to?

Actually, it was the Democrats who opposed interstate insurance exchanges. The reason is that if an insurance company could sell policies across state lines, they could effectively get around state laws that they didn't like. For example, if Texas passed a law that the insurance companies didn't want to follow, they could charter in Oklahoma and sell insurance policies to people in Texas without having to worry about Texas law.