That's correct. Their position is that every time "Single Ladies(Put a Ring on It)" (...all the single ladies...mmm, what a jam!) goes off on your bling, bling iPhone, that you now owe Beyonce a royalty fee. That is, so long as you are out in public when your cellphone ring, so that other individuals are able(forced) to hear it.
Various responses to ASCAP's absurd and nonsensical (or is that overly redundant?) claim has been swift, and for the most part, relatively fair in its criticism. Techdirt points out that this claim hearkens back to ASCAP threat to Girl Scouts regarding the singing of various campfire songs at troop meetings, and that by posing such a claim against, ASCAP is overreaching, and targeting the wrong party (Mr. Masnick points out...how can ATT be held liable for what their users have installed as a ringtone, and where that ringtone is played?).
I feel that this claim is more akin to the recent claim by the Author's Guild, that the text-to-speech function on the Amazon Kindle is a type of "public performance", in violation of copyright law, that will ultimately deprive author's profits from the sales of audiobooks. Both claims follow failed lines of reasoning. No one is going to put up with Kindle's text-to-speech in lieu of an audiobook read by a professional, just the same way that no one is going tolerate a ringtone instead of purchasing (or (illegally) downloading, but that is beside the point, and another issue altogether) the full version of a song.
Additionally, the EFF has responded to ASCAP, and have pointed out that even if the ringtones can somehow be construed as a public performance, copyright law makes specific exemption of performances "without any purpose of direct or indirect commercial advantage". Clearly, no one is attempting to profit from there cellphone ringtone (although, I could imagine a bum who carries around his ringtone capable cellular device, and dances to various clips when passersby call his number...).
Essentially, any claim of this nature by ASCAP should be DOA.
As new technologies continue to arrive, old media entities (such as ASCAP or the Author's Guild) continue to try and fit a square peg into an increasingly round hole. These media entities should focus on transforming their old business schemes into new money-making strategies that can embrace the functionality of new technology, instead of trying to limit or dampen its potential. Granted this is easier said that done, but still, I cannot see anyway in which claims of this nature are possibly beneficial to anyone within the music industry.