Keej,
You’re making this way more complicated than it is.
The logic of this study is very straightforward:
If P, then Q.
If not Q, then not P.
Not Q, therefore not P
Clear?
So now let’s plug everything in:
If [MMR causes Autism], then [the autism ratio in Group A should be higher than that of Group B].
If [the autism ratio in Group A is not higher than that of Group B], then [MMR does not cause Autism].
[The autism ratio in Group A is not higher than that of Group B] therefore [MMR does not cause Autism].