I used to display a very similar helicopter, for the RAF. The display was not simply me, doing something ad-hoc; everything was strictly controlled. I was selected to be a display pilot after an operational tour and two tours instructing. By then I had a couple of thousand hours and was serving as an instructor on the operational conversion unit for the type.
To "work up" to a display I was put with a previous display pilot, a more senior officer and more experienced type instructor who was already familiar with some of the more adventurous manoeuvres proposed. We discussed them one by one, on the ground.
We then flew together and he demonstrated them individually. I then practised, with him supervising as safety pilot and captain. We came back and discussed each manoeuvre on the ground again and what could go wrong, and how I would "escape" if things went wrong.
I was then sent off with my display crewman, to practice the individual manoeuvres, in a safe area. When I was happy I fully understood what I was trying to achieve with each manoeuvre, and how to do it safely and consistently, I was required to put together a proposed sequence. The manoeuvres were stitched together so the aircraft could be flown smoothly and without over-stretching it, or the crew, beyond their limits and with a margin of safety. For example, all turns were done away from the crowd.
The sequence was discussed with the other instructor. When he was happy, we were required to present the proposed display sequence to the Squadron Commander, who asked many questions and put forward a few "what ifs". The sequence was then authorised to be flown. I then flew the display at base with the Wing Commander and the Group Captain Station Commander watching. All flying was stopped for the event and the station fire crew were brought to immediate readiness.
After we had flown the sequence, twice, we were debriefed again. I was then authorised to practice the whole thing until everyone was happy to present it to the Air Officer Commanding, i.e. at Command level. We practiced regularly, at the end of the day's flying programme.
A video (from the ground) was made of the display and I was required to dub a commentary over it, explaining in technical terms what we were doing with the aircraft. This was sent to Command, for the AOC to review. A day was set for him to visit and again we flew it for him, as before. Finally, after more questions, the display was formally authorised, and a minimum base height included. I was then required to attend a joint services display safety briefing at Central Flying School, before the season began.
I displayed throughout the season, without incident, to a fair bit of acclaim. It was a fairly big helicopter and it made an impressive sight because we were flying manoeuvres not normally seen, and certainly not authorised in squadron service. We took the aircraft to its limits. Some people were convinced we were looping the aircraft at about four hundred feet- we weren't, but it was deliberately made to appear that it did, at least from the crowd line.
As an aside, I was given a couple of "non airfield" locations to display at, one of them being a large American comms base, for their families day. I was concerned about displaying there so I got permission to go off in advance to overfly and recce the site. I deemed it unsuitable because there was no crowd line, so on the day we flew in and did a static display instead. To my dismay, two other military helicopters who had obviously not recce'd, did display and carried out vertical manoeuvres directly above the crowd, which I thought totally outrageous and stupid.
The point is, in the case of military display flying, at least in UK, the whole thing is very strictly controlled. I have no reason to believe it is less so elsewhere.
It seems to me that the mistake made by the NH-90 pilot was a simple handling error on the day. He appears not to have put in enough in-turn pedal during his wing-over. The aircraft side-slipped into the turn, losing him height and delaying the achievement of his roll-out heading. By the time he realised he was too low, a very high ROD had built up and there was not enough recovery height available.