It certainly seems like your player is correct. There are many options to keep in mind, however. Points 1 and 5 are the ones I recommend.
1) Do your best to adjucate the diplomacy skill "correctly" (or at least consistently.) In order to use the skill, the opposing party or parties must be willing to at least listen. If someone simply attacks on sight, diplomacy won't have any use. I'm not saying that you've adjucated the skill in that fashion, but I've seen GMs give diplomacy too much power.
2) I would recommend against this since your player is obviously attempting to make his or her character a skilled diplomat, but per page 66 of the PHB, "Your DM may limit certain synergies if desired."
3) I doubt this argument is valid. Even if it is, I would not recommend it for the same reason as above. Do synergy bonuses grant "synergy bonuses" or "unnamed bonuses." If they grant synergy bonuses, then they should not stack. However, from my understanding, the bonuses are unnamed (and stack).
4) Reading the Diplomacy description to the letter:
Synergy: If you have 5 or more ranks in Bluff, Knowledge (nobility and royalty), or Sense Motive, you get a +2 bonus on Diplomacy checks.
Since this is one statement instead of three separate statements (according to grammar rules), you only get one +2 bonus. However, if everyone starts looking at the grammar of the core rule books, the game is pretty much unplayable (thus, this argument is even worse than the one made above.)
5) Is this breaking your game? If it is, work with the player to allievate the problem. If it isn't, let the player have fun.