Zed is strong. That is true. Now, how to go about saying he isn't OP?
-If you are a statistics guy, he has a 48% win rate. So he loses more than he wins. This is true at all levels of play, from Bronze to Diamond. I would argue you can't be over powered and yet lose more than you win in a large sample size. Especially if it remains true at all skill levels independently as well.
-If you are an 'in game' guy, it gets more complicated. Zed is pretty good in lane, though if his opponent picks Exhaust he has almost zero kill pressure. He counters some champions, and is countered by others. He has weird power spikes, where he often will hit them before his opponent, but his opponents spikes hard counter is own (Classic example is Zhonyas hard countering Zed all-in). This means if you aren't careful, he can snowball. And ANY fed assassin is scary. Yet, if he can't end the game early, he runs into two different walls, depending on skill level.
-Against higher skilled opponents that are good with counter building and active items the enemy AP champions will all have a Zhonyas to ignore his ultimate and the enemy AD champions will all have a QSS/Mercurial to remove his ultimate. They will also work as a team to lock the Zed down so he can't actually 1v1 the carries, and without his ult proc he can't one shot kill a late game carry.
-Against low skilled opponents, one shot killing a single target doesn't mean nearly as much, because your team doesn't instinctively push advantages and take objectives. The longer the game goes, the less important a fed assassin is. And since Zed can only instakill a single target (Like, say, Katarina with her 53% win rate) he can't single handedly kill an entire enemy team and take objectives himself.
So, it is clear he isn't OP. Is he 'broken' in another sense? The argument seem to be that he is low risk/high reward. Maybe in lane, but out of lane? I think his risk is way higher than people think. You see, 'Risk' isn't just personal risk, your chance of dying. It is also the chance of your action working. Zed's damage is so easily countered by a well timed stun after he ults (Easy, because he always appears behind the target, so you know where he will appear after he ults), or an Exhaust, or a Zhonyas or a QSS that I feel his 'risk' is actually rather high. If he goes for the ult-all-in in a team fight, especially late game, there is a very good chance he won't kill his target.
So for the risk of jumping into melee range in a team fight, he has a chance of killing an opponent if they don't have the items that hard counter him, don't have a support watching to exhaust, and don't have someone saving their CC specifically to blow up Zed. That sounds risky to me. The reward is obviously high, as if he succeeds he blows up a squishy and gets out.
In effect, no he isn't "broken" no risk high reward. Is his kit clunky? No, it is super thematic and fits perfectly together: Jumping all over, throwing shuriken, mocking laughs... It even has the wait 3 seconds then your enemy explodes Ninja chiche.
I'm trying to figure out where all the Zed hate comes from. Lane phase, I guess? He is hard to gank and harasses well. And he is so easy to counter in team fights that he often is relegated to split pushing, which lots of people find annoying. Also, 'He doesn't fit the mid game meta'? Seriously? No shit, he is a purposeful counter to the meta. The same way Poppy counters the meat-wall tops and Corki counters the hard carry ADCs. That is his job. Picking a metagame sheep pick and hoping you don't get countered is just stupid.