Does losing Dex to AC also apply to CMD?

Relevant rules:

CMD:

…Any penalties to a creature’s AC also apply to its CMD. A flat-footed creature does not add its Dexterity bonus to its CMD…

blind:

…The creature cannot see. It takes a –2 penalty to Armor Class, loses its Dexterity bonus to AC (if any)…

penalty:

Penalties are numerical values that are subtracted from a check or statistical score. Penalties do not have a type and most penalties stack with one another…

Invisible:

…Invisible creatures are visually undetectable. An invisible creature gains a +2 bonus on attack rolls against sighted opponents, and ignores its opponents’ Dexterity bonuses to AC (if any) …

Bonus:

…Bonuses are numerical values that are added to checks and statistical scores. Most bonuses have a type, and as a general rule, bonuses of the same type are not cumulative (do not “stack”)—only the greater bonus granted applies…

The question is: Does losing your Dex bonus to AC mean you lose your Dex modifier which is factored into the CMD?

And as a side question:
Does losing your Dex bonus to AC mean you lose all dodge bonuses (not only the one from the Dodge feat, which explicitly states that you lose the benefits of that feat if you lose your Dex bonus to AC)?

My GM has the opinion that blinded creatures do not lose their Dex-bonus on CMD, because it is no penalty. He said:

…If it would apply in this case why are there multiple special rules which explicitly address the case where you lose your Dodge bonus to AC and in addition something applies which should be the normal rule in your interpretation.

For instance flat footed which explicitly mentions Dex bonus to CMD and the Dodge Feet which explicitly mentions that you lose the benefits from the Feat (1 Dodge bonus) when you lose Dex to AC.

Not the way I see it, penalties are clearly described as penalties in all descriptions ( –2 penalty to Armor Class), in addition the removal of a bonus is not a penalty in my opinion, it means a recalculation (without the called bonus)…

Is my GM right?