What is the basis for some people's practice not to eat the food at a shiva house; is there a halachik basis for this, is it a minhag or perhaps just superstition?
There's a Rabbi Sobolofsky mp3 that says it's superstitious; there is one Talmudic quote where one sage says to another "what, you want to eat the food of mourners?". But that's not the law.
He did mention the concern that sadly, as shiva houses are open to many people and the hosts have their minds elsewhere, it's not unheard of for valuables to disappear. Hence a good policy not to walk out of a shiva house with your pockets bulging full of, well even if it's food they asked you to take.
Eating food at the Shivah House (not with the aveilim) is not a problem. It is brought down not to take food from a shivah house. (I need to re-find the source)
It is brought down not to eat together with the aveilim.
Some have the practice not to bring food out of the shiva house [Aruch Hashulchan 376:11] if the person died at home [Tzitz Eliezer (Even Yakov no. 44:4)]. However, many are lenient about this [Yosef Ometz p. 192].