I would just replace that valve (and probably the flapper too). They are cheap enough and from your description it can't be working right. Make sure it is installed and adjusted per specification, and you should be all set.
Firstly, you don't want it held down, holding it down is what is true when the tank is not full and therefore, it will open the fill valve to fill the tank. This means water running. You don't want water running 24/7 in your toilet, this is bad.
Now, when it is all the way up, it should not be running at all, but since (when water is being used in your building), the change in water pressure APPARENTLY is enough to starve that valve, just enough it squeals. At least this makes the most sense for what you've described.
Now, the reason why I noted to replace the valve seat is because the water may be trickling out just enough that the fill is barely on. This coupled with water pressure change......
Also... I'd be curious what size pipes are the water supply side to the things in the building. There really shouldn't be a big pressure change when one other thing is in use and your toilet (supplied by 3/8) shouldn't see a drop. But it does. (based on your description).