Deoxyribonucleic A.C.I.D. said:
They don't have to. They just also happen to have this option. As KB said, if a heel is on a higher tier than the face, they shouldn't cheat. If they're on the same tier, they should cheat and if the face is above them, then they should do absolutely anything in order to win.
Here's a good example. I think Edge defeated Rey Mysterio clean at the 2008 Royal Rumble. At the same night, Randy Orton also defeated Jeff Hardy clean. Why? Because Orton and Edge > Jeff and Rey at that point. However they both needed heel tacticts to prevail against Undertaker and Cena/HHH. That for me, was perfect heel booking.
But not all heels should cheat. Monster heels shouldn't cheat. A monster heel should win his matches clean. What seperates a monster heel from a face though, is that he will brutalize his opponent before or after the match and maybe during the match. A face should never brutalize his opponent in order to cause him a severe injury. And that's a problem with today's wrestling.
Cena was an absolute asshole/heel back in 2010. He defeated Batista with a freaking ducktape in a Last MAN Standing match. He almost killed Batista in their I Quit match, even though he had won. He constantly bullied the Nexus. Broke his own word and didn't retire and then almost killed Wade Barrett even though Nexus was officialy over.
So to sum up, a heel isn't only decided upon cheating. Character, post-match behaviour, how they take a loss, how they treat a victory, trash-talk, crowd interractions, storyline, unethical decisions. All of these aspects are what make a heel. Cheating is just a part that exists mostly to protect the face, rather than to give the heel actual heat.
But as I said, a heel should cheat when it's needed and he should be his own man, when he can.