Nextel's iDEN system DOES cause audible interference on powered audio amplifiers...like headphone amplifiers, or small speakers on a computer...it sounds like, as best I can describe it, a "fluttering white noise of static". It's not direct interference with an AM or FM signal, it's purely something happening in the speaker amp itself...but whatever it is, it's from the RF the cellphone itself transmits because it begins the instant the phone call technically starts (as in, before the phone even begins ringing).
The iDEN system is, supposedly, being phased out as Sprint fully absorbs Nextel. iDEN doesn't work terribly well for high-data applications like 3G anyways.
FWIW, the TDMA-based GSM systems (T-Mobile, AT&T Wireless and, previously, Cingular) also cause audible interference from their RF emissions. The difference is that GSM's interference (which sounds vaguely like "dit-dit-dit, dit-dit-dit, dit-duuuuuuuhhhhhh, dit-dit, dit-dit-dit") will actually show up ON TAPE, wherever iDEN only affects the speakers.
That's one big reason why I switched away from Cingular and back to Verizon Wireless a few years back. The CDMA system that Verizon (and Sprint) use doesn't cause any audible interference. Frankly, IMHO it's better at 3G data, too...but I know that's a highly subjective analysis.
Based on the description given, though, I don't think it was iDEN interference you were hearing. Sounds more like someone left a mic on somewhere they shouldn't and it was being added to the final mix. In other words, it
seems to me to be more like human error than technical interference.