You are essentially correct
The key is that desecrate specifically says "Each Charisma check made to turn undead within this area takes a -3 profane penalty," (later modified to -6 by the presence of the appropriate altar).
When you try to turn, you do these things:
- Make a Charisma check (your "turning check")
- Look the result up on a table. If the result on the table is high enough to potentially affect any nearby undead, proceed to step 3.
- Roll turning damage (not described as a charisma check, though you do add CHA to it)
- Apply damage, adjudicate effects.
You correctly identify that the penalty is normally applied to the Charisma check in step 1.
However, note that if all skeletons had at least 3 hit dice (or turn resistance, or were bolstered, etc.), you still would not have been able to turn anything. I would avoid jumping to the conclusion that your DM was "wrong" here, even from a very strict rules-as-written perspective.
If it bothers you, you should likely spend a short time before or after your regular game-time talking to your DM about how it works. And hey - if he really does want those bonuses to go directly to HD values, consecrate and various other bonuses to that check will make you an undead-turning beast!