No, there is no longer the "or more is a 2" part about the specific roll in question then. Here, the roll of 6-X.
You must ask for a roll which is an element of the set of rolls which contain the number 2. The only specific roll which can satisfy "at least one die is a 2" is when only the first die is seen, and it's a 2. This allows for the roll to satisfy "at least one die is a 2". The other die could still be another or the more 2.