Not everyone is familiar enough with social media to make the best educated decisions.
It may very well be that the friend's mother wants to add her daughter's friends as a way of keeping tabs on her daughter's online social activities.
I don't think this an unreasonable approach, although it doesn't guarantee that she'll be able to see any inappropriate behavior.
The privacy functions on Facebook, while crude, and far from actually providing privacy, have some flexibility. It is not difficult to hide posts from people you have friended (of course, the counter to that is that it is not difficult to see posts from a friend who is trying to hide posts from you... or even someone who isn't your friend!).
In fact, I'm not sure I understand the benefit of not planning to friend your own daughter. Is this intended to allow her some privacy, so she can feel like you trust her, or is it to spare her any potential embarrassment from having her parents listed as "friends"?
If it is to give her some space and independence, I'd suggest an alternate route: friend her, and then go over the privacy settings with her, and show her how to hide posts from you.
Having her listed as a friend is helpful if one or both of you use the site with any frequency. The private messaging alone might justify it, plus it could become a healthy outlet for you to strengthen your relationship with her (yeah, that might be a stretch with a 15 year old... but it could happen!).
More importantly, though, it is good to discuss safety and privacy with her, so she is aware of what is and is not possible, what general best practices are, and what the risks might be. Presenting this dialog in the context of "here's how to hide stuff from me" shows that level of implicit trust you may be trying to convey, plus makes the whole conversation very non-confrontational.
You can also use the friend's parent as a demonstration example: have your daughter accept the friend request (which will likely make a better impression on the mother than ignoring, declining, or blocking the request!), and then go through changing the settings to hide the friend's mother's posts, and hide your daughter's posts from her.
In either case, be sure to emphasize that none of the privacy settings in Facebook are fool-proof (I'm not sure if it still is the case, by one easy way to bypass restrictions was to send a friend request; until the other person expressly rejected it, the request would give you access to content as if the request had been accepted). Discuss social engineering scams, the possibility of people impersonating people she actually knows, what happens if someone else gets access to her account, or one of her friends' accounts, and the possibility that she might some day have to show her account to a potential employer.
If you aren't aware of all of these things already, look them up and familiarize yourself with these very real risks.
Make sure she understands that the only way to keep information truly private on Facebook is to not post it there at all.