I have a few (probably unpopular thoughts on this topic. If the student in question was considering quitting Aikido over 'fear of hurting someone', I think that fear needs more exploration other than 'well, people get hurt' (and I have some unpopular thoughts on that as well, later).
Why is she so afraid? Has someone hurt her on the mat? Does she have trouble controlling violence within herself? People that have that degree of fear of injuring someone, in my experience, are wither very large and/or hot tempered, and have hurt others a lot in the past (off the mat, intentionally or not), or they've been unduly pounded as uke, or their ukemi is shaky enough that they associate training with getting hurt. I am one of the most pacifistic students around, and have sat out techniques when instructors want us to hit uke after we have them subdued, but I do not worry about hurting someone. Now this may be due to the fact that I am small enough that my punches don't mean much, and I feel like I can control my technique enough (poor that it may be) so no one gets hurt.
As for the inevitability of training injuries---yes, people may occasionally get hurt, but it is very very rare, or else a dojo is not stressing appropriate ukemi enough. Ukemi is what saves us when things go wrong, that and training at the level of our partners. I think that part of Aikido is an understading of our partner, and sensitivity to them as well as caring about them. If all those things go into training, it should prevent most training mishaps. So rather than take the view that 'well, if you train you hurt and get hurt' I'd take the view that 'if you train with sensitivity and connection, and if you have to, go really slowly, no one should get hurt'.