The veggies you need to watch out for (on the HCG diet) are the ones that are starchy, sugary or have too many carbs...
You really need to watch out for this in Phase 2 and Phase 3 of the HCG diet.
Mushrooms are not starchy or sugary, however they do have quite a few carbs, so they were not included as a part of the diet.
Just go with the original 13 vegetable choices, there are plenty of choices there for you not to get bored while on this diet.
You should be fine eating them.