They had repeated successful demos of it, but NASA kept adding on new requirements while implicitly signaling that they had no interest in approving the system, which would have made Boeing's lander look obsolete before it was ever finished. NASA's judgements are heavily influenced by external factors that make it quite difficult on outsiders, while enabling reckless behaviors for insiders.
For example NASA deemed the Boeing crew vessel safe after its pad abort test resulted in only 2 of 3 parachutes deploying and it suffering a propellant leak - all in beyond optimal conditions. They deemed it not only safe, but safe enough to completely skip the scheduled in-flight abort test. All of this is of course how you ended up with astronauts trapped on the ISS that had to be rescued by SpaceX.
For another contrast there after SpaceX did swap over to a simple parachute system, their pad-abort test went off flawlessly. NASA still required they do an in-flight abort. Granted, that's nothing to complain about, because that's exactly what NASA should do. But they also should have had Boeing completely redo their pad-abort test and damned sure do an in-flight abort as well. Safety culture at NASA is generally completely dysfunctional because of non-safety factors.
This is nothing new either. Both Space Shuttle disasters were 100% preventable, and not only in hindsight. Engineers brought up the exact causes of both explosions well before they happened, but the bureaucratic layer ignored them.
I'm not entirely understanding your point. Are you saying they were able to demonstrate a better than 1-in-N probability of fatal mishap for the appropriate N (I believe about 300 for this case) and NASA just wouldn't accept it? Or they weren't, but ???
Shuttle is an excellent example of the sort of thing I'm talking about. It had no abort capability in the event that something went kaboom, and no realistic abort capability at all for large critical portions of launch. Their test pilot outright refused to test an abort because he didn't think it would be survivable. It never should have been human-rated, and it only was because NASA pretended it had an abort capability that wasn't really there.
Starship is even worse: not only does it have no realistic abort capability for most of the launch, it also has a very delicate landing procedure that requires a substantial amount of propellant to remain on board, no ability for the occupants to escape in the event that those propellants decide to mix in a place where they're not supposed to, and very limited ability to handle engine failures.
There is no exact and objective set of hoops one can jump through to prove a sufficiently complex (let alone novel) technology safe within a certain bounds, short of doing exactly what it will be doing over a large sample, which is often not economically feasible. In fact one of the first things that happened early on in the Apollo program is that mathematical risk modeling was completely scrapped. The results were always so pessimistic that NASA found it impossible to move forward with it!
So this leads to judgement calls from NASA that are opaque and, in practice, are not necessarily grounded in safety, as per your own example as well. NASA clearly did not want SpaceX doing propulsive landings and was making sure to dot all their i's and cross their t's with them, while simultaneously going YOLO with Boeing and actively greenlighting their vessel which clearly was not even remotely safe for a human. In this context, it's highly unlikely SpaceX could have convinced NASA to more forward with the propulsive landings, even if they were the safest thing ever invented.
For example NASA deemed the Boeing crew vessel safe after its pad abort test resulted in only 2 of 3 parachutes deploying and it suffering a propellant leak - all in beyond optimal conditions. They deemed it not only safe, but safe enough to completely skip the scheduled in-flight abort test. All of this is of course how you ended up with astronauts trapped on the ISS that had to be rescued by SpaceX.
For another contrast there after SpaceX did swap over to a simple parachute system, their pad-abort test went off flawlessly. NASA still required they do an in-flight abort. Granted, that's nothing to complain about, because that's exactly what NASA should do. But they also should have had Boeing completely redo their pad-abort test and damned sure do an in-flight abort as well. Safety culture at NASA is generally completely dysfunctional because of non-safety factors.
This is nothing new either. Both Space Shuttle disasters were 100% preventable, and not only in hindsight. Engineers brought up the exact causes of both explosions well before they happened, but the bureaucratic layer ignored them.