Hmm, I think there are a number of factors here. I'm a music teacher with some contact with the ABRSM BTW.
It sounds to me like the fundamental problem is that your violin teacher is just not steeped in the culture of exams. If he was going to enter her for the exam, he should have known the general standard required, and known of the normal problems kids' face doing their first exam, such as panicking about sight reading. All of that should have been taken into account. She should have practised with him attempting the sight reading NO MATTER how bad the attempt. As has been said earlier a minimum of 1/3 marks is given for any attempt.
The fact that he "forgot to enter her" the first time chimes with this. It doesn't sound like he's the kind of teacher who's doing that all the time for lots of students. This doesn't mean he's a bad teacher of course - there are many different, valid ways of teaching. But he needs to know that failing an exam can be very distressing for a child, and if he's not up to overseeing it properly, he shouldn't be entering people.
It's rare to fail grade 1, and FWIW I have heard ABRSM examiners say that when it happens, they consider it purely as an indictment on the teacher, not the student.
There's also another issue, which is the huge difference between the many ways that "musicality" can be expressed in a free and creative fashion, and the incredibly tight-arsed structure and culture of ABRSM exams. There is an enormous gap between a student being able to "do something" in the sense of getting their instrument out when they're ready, having a chat, warming up, playing a bit, eventually finding their way and doing something quite engaging and creative; and going into a 12-minute exam and being told "you have these notes and only these notes on the page, you have one chance to play them: start NOW!" I know I have been guilty of underestimating that gap before, I think it's very easy to do because you get caught up in the pleasure of hearing creative kids do interesting things.
It's terribly important to remember that an exam's validity is only in relation to the parameters it set up for itself in the first place. A "music exam" is a test of SOME musical activities, VERY strictly defined and examined at one time. It's not, in any way at all, a test of "musicality". You can be naturally far worse at something than someone else but if you're put in a competition against them for which you know the rules you are being judged by and they don't, you will win.
I have sympathies with both sides of the pro/con exams debate. I certainly think there are a lot of children who are not suited to them; a lot of young children are forced to take them too early; and parents often make the mistake of attaching wider importance to them then is really merited.
Having said that, the violin is a very classical, reading-based instrument. If she enjoys it and is likely to want to take it further, then that's probably going to happen by reading music in an orchestra, not by jamming in a rock band. There's a case for pushing a structured exam-based approach more than one might on some other instruments.
I think I might look for another violin teacher, while simultaneously investigating other, less formal kinds of musical experience. Get a guitar and learn some chords; join an African drumming group; that kind of thing. If she's going to do the classical violin she needs to do it properly; but she may be more tempermentally suited to doing something else.