When people are talking "press forces and ratings" it is easy to quote numbers without really appreciating what they mean. And if the frame is distorting then it may be strong enough not to fail, but is certainly not STIFF enough to hold its shape!
Of course, Manufacturers have reputations, safety legislation etc. to consider when they make and rate their goods. We do not always follow those rules (do we even know the rules?) when we make stuff in the workshop, so just be careful.
While I absolutely agree with what you say I wasn't kidding about the rating (8 posts back up). Here's a vid of a similar press in action. Note the die area he is squeezing with - he's not punching. Note at about 2:30 how the stiff high carbon steel heats back up to yellow with the internal molecular friction of the applied force. Like you say however this requires a massive stiff frame and a well thought out rigid design. As you allude, most weapons have a "stored energy spring" of some sort (metal, air etc) as the initiator! A weak frame could also be it's own trigger.