A finding that people who perceive corruption to be widespread also want more government regulation would be difficult to explain if regulations were simply facilitating rent extraction by bureaucrats.
Is it really so "difficult" to believe that people could favor policies with consequences they oppose? Couldn't you just as easily write "A finding that people who favor price controls are opposed to shortages would be difficult to explain if shortages were simply caused by price controls"?
Oliver Cromwell famously said: "I beseech you, in the bowels of Christ, think it possible that you may be mistaken."
For modern political economists, I'd like to add: "I beseech you, in the bowels of Bastiat, think it possible that voters may be mistaken."