Mobile phone interference

Is it true that the mobile/cellular phones that interfere most with radio and other signals do that because the phone itself has a stronger signal? And if not, why do they interfere with radio signals?
I realise that isn’t phrased very coherently, but I can’t think of a better way to put it. Sorry.

Stronger in what sense? In terms of absolute power I doubt that many mobile phones are as powerful as, say, a transmitter for a radio station, but it’ll depend how far from the source one is.