When somebody points out that the excuse you just gave is not plausible, you admit defeat and say "I meant my other Grandma" to offer another, alternative but also implausible excuse.
Comes from the Irish soccer player Stephen Ireland, who refused to play a match as he said his Grandma had died. When it was proven she was alive, he then used the excuse "I meant my other Grandma" (who was also alive).
"Hey dude, want to go and grab a beer?"
"I can't, I have to study for my exam"
"We don't have any exams until April"
"I meant my other Grandma"
"Want to go catch a movie?"
"I can't, I'm meeting Leo"
"Leo is on vacation in Mexico"
"I meant my other Grandma"