Well, actually, it could be argued that he's right, from a purely legalistic point of view. Feudal oaths contained no "depending on how much I like you" formula. However, I don't know if oaths of fealty specifically mentioned numbers of troops! (I think near-100% was implied.)
Also, I believe that vassals owed homage to their king in addition to fealty.
Three misconceptions:
1) Oaths of fealty are a *bilateral* contract. Just as the vassal owes service to the lord, the lord owes protection and property to the vassal.
2) The vassal of my vassal is NOT my vassal. Vassalage does not transfer and is not hierarchical. In practice it might often seem that way, but in fact and tradition it was not. A knight might have been in the army of the Duke of Whatsit fighting a war started by the King of Wherever but that is not why he was there. He was there because a local Baron who was his feudal lord and from whom he held land owed fealty to some Earl, who owed fealty to a Duke who happened, at the time, to find that his cause coincided with the King's. If the Earl broke the feudal contract with the Baron (for example, broke a pending betrothal) then that knight was likely marching home and neither the Duke nor the King had anything to say about it outside of trying to convince the Earl to uphold his oaths.
3) Vassalage was not hierarchical. One could very well be both lord and vassal to the same person for different lands and titles. One could be vassal to both sides in a conflict (very common). CK2 obviously chose to avoid this mess altogether but it's helpful to keep in mind when thinking about how the game "should work" to be "more realistic". Sometimes you can't model history precisely in a computer game.
Also it was very common for a vassal (esp a powerful one) to just not show up when called upon. Are you going to go halfway across nowhere and face him in the field or siege his castle just to force him to bring his troops? Nope. Now it may be that he miscalculated and that you will be vengeful if you win, but in reality this happend constantly and vassals got away with it constantly
Likewise it was entirely common for a vassal to send the minimum required or just pay off the obligation in coin (scutage).
[I think that would actually be a cool/frustrating addition to CK: "A messenger arrives from Duke Jean of Burgandy with his apologies that he is not well positioned to muster his men due to the late harvest and omens of a hard winter. He has sent 57 gold coins in scutage to support your war effort."]
I think the CK system of basing this on an approval rating is a good abstraction. Treat your vassals well and you can rely on them when you need them. Treat them very well and they may support your cause enthusiastically. Crap on them (or just have a troublesome vassal who is too ambitious or has unfulfilled claims) and they will do only what they must and sometimes not even that.