I would tend to agree with @KatMT and @uskoolfish that there are many in arts admin positions without a degree in it. However, there is such a range of positions that it will vary tremendously. If by arts admin you mean working in an entry level position for something like broadway dot com or an agency, that’s probably true. And those positions are not necessarily very well paid. If by arts admin, your student is interested in starting a theatre company, or after years of successful productions with said theatre company, they are in a position to hire well-qualified individuals for positions as director of advancement, general manager, associate artistic director, marketing manager, production coordinator, etc., then you are likely to be looking for someone with more extensive experience and not just a degree in arts admin. 
An additional major is never going to be a negative, in my opinion, in either direction and if she’s interested in pursuing arts admin seriously, then there will likely be other things she can do to enhance that major once she’s out in the real world. If you’re interested in having a look at the staff at the theatre company that I’m involved with, I’d be happy to send you a link @katew529 .