True or False:

The multi-cellular stage in the life cycle of a fungus is haploid.

http://staff.jccc.net/PDECELL/celldivision/lifecycles.html#fungi

Yes, true. And to make it more interesting, there is a species of fungi that live in symbosis with orchid seeds (which have no endosperm)...the haploid fungi invade the orchid nuclei, and it the right ones join up to make a dipholid reproductive fungus, it produces simple sugars as a byproduct that allows the orchid zygote to develope to a seedling. Orchid seed provides the enzymes, fungi in mating produce food for orchid seed. Nice sweet touch both ways.

That was a test question. Your answer agrees with the professor.

The multicellur mycellium of basidiomycetes is primarily dikaryotic, so I picked false.

My professor said that the nuclei are still haploid so the statement is true.

Of course the nuclei are haploid in a dikaryotic cell, but I would still consider the stage as a whole to be dikaryotic and not haploid.

So, am I wrong?

The nuclei are indeed haploid. At some times, there may be two nuclei, each haploid, in a dikaryotic "cell". (Some argue that this structure is not a cell)
This is the danger for true/false questions, sometimes the answer begs for explaination. You knew too much to answer the question simply. It is not worth hiring a lawyer over it.