Water is a hydraulic fluid! Jebus...
Hydraulics is the utilisation of the power of fluids/liquids to transfer energy and carry out work. In that sense a hydraulic fluid could be tomato ketchup, urine, tea, whisky... any liquid really. It just so happens that if you try and use a crane which uses Tetley as the fluid it might not work quite so well as an oil which has been specifically designed to deal with massively high pressures while not compressing, getting hot, leaking past seals and lubricating seals.
A bicycle brake isn't quite the same. If I ran a maggy these days, I'd happily run tea in mine just to prove a point...
Brad- Have you tried a water bleed before?