Actually, there seems to be both a very deliberate distancing of Morty and a possible mistake later on, that shows that neither character is from C-137.
For Morty, the character specifically states that in his original dimension, Rick gave up after turning people into mantises. Which, in the show, isn't what happens. They only abandon their dimension after everyone gets croneberged (and honestly, we don't even know if that was really his original universe either, it's Rick and Morty, anything is possible). Plus, Morty doesn't know what the monsters are, Rick has to tell him they are cronebergs.
As for Summer, I think this is more likely a mistake by Ferdafs than intentional, but in the 3rd section of the scene, Wild Summer is suspicious of Tammy, and makes a reference to bird person. But the tammy/brid person thing doesn't appear in the show until the last episode of the first season, way after the world gets croneberged. And we don't find out Tammy is a traitor until the end of season two, so wild Summer would have no reason to be suspicious of her, or know that she liked birds. Unless, events happened differently in her universe, in which case, she can't be Morty C-137's "original" Summer.