To answer your original question, as a general principle the standard for operation of power presses in Canada (and elsewhere) does allow the use of hydraulic die clamping but there are requirements for how it is supposed to work included in the standard, because of the obvious safety consequences of what happens if the tooling detaches from the machine while it is running. Hydraulic die clamping is standard practice in the automotive industry in large power presses for quickly changing out the tooling between, let's say, left front fenders and right front fenders and left front door panels and right front door panels, all in the same machine. (The whole tooling set for each piece to be made is on a die cart, unclamp the outgoing one, wheel the whole set out of the way, wheel the next one in, clamp it up, carry on)
But as for the tooling in your photos ... yep, that's scary.