That statement is so wrong in its entirety, it's actually funny.
If bot wins hard, and the enemy has an assassin mid, bot lane is irrelevant.
Would like to see a zed getting close to the enemy kog maw, when there is a Lulu, Janna or Nami beside him. It only works if the support is doing a bad job.
If top wins hard and mid has a mage of any kind, top lane is irrelevant.
Bruisers and Tanks counter mages so hard, especially when they are fed. Do you even play the game? Mages are so ridiculously squishy, the moment you get close to them and touch them, they fall over.
Mid lane decides the outcomes of games almost entirely by themselves.
Actually mid lane only decides the game if one of the 2 mid laners is far better than the opponent.
Mid lane usually takes a lot of jungle help to work sufficient. You can't just roam bot without losing a lot of value in midlane these days. Especially with tower platings being a thing. It's just too risky if your jungler doesn't hold mid. Especially when you play a mid laner that has a sub-par wave clear, but good roaming abilities.
If there is a role that can "carry games by themselves", I'd say it's jungle with early to mid game pressure and adc in late game. You can't tell me a mage can 1v5 no matter how fed the mage is. Mages are (almost) all about damage, which they need to scale into late. Building more defenses to survive fights longer comes at the trade for less damage. Meanwhile most ADC are highly mobile, deal a lot of damage (especially late game) and have life steal which peps them up again when they take some damage.
Mid lane is in no shape or form op. There are a few culprits that need to get tweeked, but that's about it. The role itself is completely fine and relies mostly on the jungler to help them out.