The cheating by one does not absolve the cheating by another.
No, it doesn't. That said, the point is less about absolving one team and more about pointing out a degree of hypocrisy in claiming "4 legit titles" when it's not even particularly challenging to find incidents of rule breaking by the supposedly legitimate team.
Clearly the Patriots broke rules at some point (although to this day there's questionable evidence at best that they were ever broken during a year when they actually won the Super Bowl). I don't think even the most diehard of fans will deny that. And, hey, if that simple fact on its own is enough for you to want to toss out all credibility in regards to their accomplishments, more power to you, I suppose. But at least be consistent with it. I'd wager that I could fairly easily go back and find some incidents of knowingly breaking the rules to implicate virtually any and all Super Bowl winners. So if you want to dismiss the Patriots, go ahead. But you should also be dismissing the 49ers of the 1980s for the aforementioned reasons, the Steelers of the 1970s for widespread steroid usage, the Cowboys of the 1990s for circulating a team program to allow players to take banned substances, the Raiders of the 1970s for having doctors disperse PEDs among players and...quite literally having a sign in the locker room saying "cheating is encouraged," numerous teams for circumventing the salary cap, numerous teams for intentionally falsifying injury reports, etc. Plenty more I can cite if that's somehow not enough.
Just, y'know, be consistent.