RCD's save lives but there's no guarantee, some people die from shocks of less that 30mA, it's just a numbers game where most will survive but some won't.
Older fuse boxes often don't have RCD protection, only overload protection. The fuses in them only protect the circuits from overload damage, they don't protect people from getting fatal shocks.
All the UFH controllers I've experienced are just a temperature control, they don't include shock protection or earth leakage protection. Technology progresses and systems are constantly made safer so I'd be interested to read up on the controllers you refer to if you can give me a link.
People getting shocks in a bathroom are far more likely to be killed than in other locations. The electrical regs recognize this and address it by declaring bathrooms 'special locations' that require extra protection measures.
It probably is statistically unlikely to get a shock from an undamaged UFH system as you say but if the wire is damaged under the floor and there's moisture around the damaged area it's highly likely it would cause someone in bare feet to get a shock. There's many variables involved so it might just be an occasional tingling or 'static' sensation when touching taps or a towel rail or it might be worse.
My advice still stands, if the UFH heater tape or wire is damaged I'd strongly advise an official repair by someone with experience who can test the system afterwards.