Toilet won't fill if water supply is on high
I've had a similar problem and it was due to an "Auto Burst Detecting" supply line.

Something similar to this: http://media.wattswater.com/F-FloodSafe.pdf

The high flow of water is "Detected" by the FloodSafe line.  This causes it to trip and shut off the line as it thinks the high flow of water is caused by a broken line.   My solution was to just leave the valve partially off and live with the long toilet fill times.

Note: Leaving the valve partially off will most likely defeat the purpose of the FloodSafe line (As it cannot have high enough flow to detect a burst line).