I can understand why they are making it a requirement, although stating no "audible" accent is stretching things.
Many a time I have had to contact an office, especially a government office, and the individual who answers the phone has such a heavy accent I cannot understand them. When that happens, I ask if I can speak to someone else and if they won't transfer me I hand up and call again with the hopes that whomever answers the second-time around is someone I can actually understand. I have problems with some clients at work as well calling and asking questions. I feel bad if I can't understand them but I can't help them either. I will usually ask them if they have an email and to email me their question(s). Even at that, if English is their second language, that's not always helpful either - spelling and grammar can also be an issue but at least I get a sense of what it is they want or need.
So, while it may seem discriminatory, its good business as you want someone who can communicate with your customers. Again, I think likely everyone has an accent. As lone wolf stated ... if you're from New York or Los Angeles. I think the point here though is how strong the accent and can people understand what is being said.
What would be a practical/alternative solution?
