That's just the explanation of eukarya which lists animalia within the same super-group as fungi and plants being in a different one altogether. Any relationship with plants to humans (which are within animalia) or mushrooms could be a bit subjective.
Yes, fungi are closer to humans than plants. If you look at the reproductive cycle of all three though, plants have a closer amount of "sexes" to humans. Plants generally having "1" or 2 sexes; humans having 2. Fungi though...