Logical fallacies and twisted interpretations abound.
A familiar must be AT LEAST adjacent to you. That their abilities continue to work when they are in the same square does not redefine "adjacent." It's just common sense.
That Tiny creatures must enter your square to attack you, likewise does not redefine the word. The game abounds with special attacks, spells, features, etc., that are exceptions to the rule without redefining the rule.
That what the player wants to do is not entirely game breaking is irrelevant to whether he is using a word within its actual meaning. The GM may allow the strategy anyway, but still want to know the meaning of the term.
Adjacent in the game takes its meaning from these two Merriam-Webster definitions:
b : having a common endpoint or border <adjacent lots> <adjacent sides of a triangle>
c : immediately preceding or following
It does not count the squares touching the squares that are adjacent to your square. If you allow that, where does it end?
"Well... now I think the squares touching the squares that touch the squares around my square count as adjacent, too! Yeah. In fact, everybody in town is adjacent to me. I think I'll make one roll and try to hit them all at once."