There are definitely counter picks in this game but to say you're pretty much 100% screwed isn't the case. Did a ranked game a couple days ago where I was Vayne with a Nami Support and the enemy team picked Cait + Zyra. That is just a brutal lane to go against as Vayne, so I asked our top lane (who was kennen) if he would swap with us, which he did. We proceeded to 1v2 the enemy top lane who was Singed, got first blood on him by about level 3, got tower early, then lane swapped back.
Now, I could have laned against the Cait/Zyra straight from the beginning but then I would probably be behind in cs a bit, probably wouldn't have gotten the first blood, hell, maybe I would have given up first blood because that combo is really tough for Vayne. They definitely have the advantage 2v2, but it's still doable.
It's also why you see many first picks of Jayce, Kennen, Renek, Shen, etc etc because they really don't have "heavy" counter picks. They have soft-counters (well, not jayce lololol) but overall it's not that big of a problem. Where as if I first pick Singed for instance and get a Teemo top with a Sejuani in the jungle I basically fucked myself over because Singed vs Teemo is rage worthy and Sej is also very strong against Singed due to her perma slows.
Then again, all these counter picks can be completely shut down if you get an early jungle gank and kill them.