There is a מנהג to eat fried food on חנוכה as a זכר to the נס of the פך שמן. Eating food fried in anything but oil, then would be a less than optimal way of observing this מנהג.
Those who made their Latkes with schmaltz (probably a relatively recent innovation, which has been, like so many others, artificially and incorrectly invested with the aura of “Mesora”), therefore, are the ones who are in the wrong.
The analogy to switching from Nusach Sefard to Nusach Ashkenaz, therefore, is quite appropriate, since Nusach Ashkenaz is the one with a real Mesorah, and Nusach Sefard is a relatively recent innovation that does not even pretend to be based on a Mesorah going back to אנשי כנסת הגדולה. This is why Rav Moshe Feinstein ruled that one may switch to from Nusach Sefard to Nusach Ashkenaz but not the other way.
There is also a מנהג to eat dairy foods on חנוכה as a זכר to the נס of the מלחמה (and the story of יהודית).
It is proper to combine these two מנהיגים so as to express the idea (put forth by the Maharal and many others) that the purpose of the נס פך השמן was to demonstrate the miraculous nature of the military victory.
Applesauce, on the other hand, has absolutely no basis in מנהגי חנוכה and is only being eaten for תאוה, which is part of the legacy of the Yevanim.
It is probably for this reason that Hashem ברוב חסדו וטובו made it that Latkes taste so much better with sour cream than with applesauce (and, in fact, even plain is better than with applesauce).