The hardest thing though is that interviewers are generally all different, and they have to be opinionated in order to be able to make hiring decisions. So you're taking a risk regardless, and have to judge the trade-off in going off the standard path for yourself.
In this situation I would have expected the candidate to offer suggestions in what to do instead, particularly because I cannot expect to understand his or her reasons in detail. If you want to seek an alternative, you should ask questions to find out exactly what the interviewer is hoping to gain from a phone interview, and be prepared with an appropriate set of alternatives to suggest with the interviewer's goals in mind. Use email, online chat, or whatever else you want that isn't too inconvenient for the interviewer. Try not to stretch out the conversation too long out in time.
Work samples are a way better indication of candidate quality than phone interviews. If the interviewer is sensible and has the flexibility to deal with it then they would definitely prefer you to show them your coding chops than ask you a bunch of technical questions. Many employers won't have the luxury of being able to spend someone's time reviewing your code though, or if they're big enough, will likely have a bunch of HR hoops to jump through.
If they're small and smart though, it's definitely worth a shot. Phone interviews are horrible for both ends. Beyond the real basics I think it's better to avoid them.
In short, be upfront and completely honest. Some people really struggle on the phone, that's life.
That being said, the same concept wouldn't necessarily apply to face-to-face interviews.