I think a better characterization of the fallacy is that it is indeed a non-sequitur, but it hides the "provided n meets some criteria" by bamboozling you with

I think a better characterization of the fallacy is that it is indeed a non-sequitur, but it hides the "provided n meets some criteria" by bamboozling you with "arbitrarily chosen" elements from a set of n+1 so that you might fail to spot where you need 3 elements in a set that potentially has a cardinality of 2.