Yes, the no spot policy is new, but in reality, they will spot rarely....I saw them do it the other day just once.
.....
Keep in mind that spotting for completion and spotting for shapes/technique are different. The coach may have been spitting the child on a skill she already consistently throws by herself to show her the correct position her body should be in. This is different than carrying her on a back handspring to let her complete it and feel she is learning it.
In general, non spotting progressions that allow a child to work incrementally will result in less problems with fear. It also gives a logical place to go back to should fear occur. In fact, the initial spotting of your daughter on this skill could have exacerbated the issue and frustration in the first place.
What happens when you spot a child is they rely on a certain cue (propriception) and visual feedback of your placement to orient themselves. On balance beam, this particularly affects their sense of what they need to do to complete a skill because of the nature of the activity. Of course, relying on additional feedback to do something is an extremely valuable tool in gymnastics because it can allow us to help a child achieve correct positions when they wouldn't otherwise be able to. But the problem on beam comes when spotting for completion. Beam is a highly mental game and the kids need to develop a system of visual, proprioceptive, and mental cues to consistently "stick" something. When you're trying to stick two "somethings" in a row it obviously becomes that much more complex because a mistake on the first thing will affect the second.
So when a coach spots a child on a BHS BHS on beam, they may be able to back their spots away and the child does it that day, but then the child doesn't develop a series of cues that is necessarily able to be replicated in other circumstances. They also have no logical progression to fall back on to "remind" themselves what the correct cues should be. So they become lost and even more frustrated because they feel they "should" have it since they did it that one day. So, I think your coach noticed how this approach didn't work for your daughter and an approach where she develops the correct timing through unspotted progressions is better for her. This is good!
Also, regardless of the method used, I can tell you from personal experience that it isn't uncommon on beam to do something one day with adrenaline and not be able to do it again because you realized you felt "lost" even if you managed to somehow make it. It's kind of like an allergy is how I describe it...it doesn't happen on the first exposure, it gets worse with subsequent exposures. The only thing you can do is back the progressions up and figure out where the problem is and correct it there.