Umm…a couple of seriously geeky points:
One phone on it's own is unlikely to affect a plane, however if everyone on board had their phone on the ammount of data being transmitted between all thouse phones and any BTS is rather likely to affect the electrical systems on board an aircraft (like when you put your phone too close to your hi-fi and you hear that daaa da da da da dadadadadada noise).
Secondly, hospital pager systems work on markedly different frequencies to mobile phones and only transmit/recieve data when required…umlike a mobile phone which regularly 'chats' to the network without your knowing about it.
So who knows? Maybe there really is 'some' truth in the warnings. Actually…annecdotally, my sister is a nurse, when she worked on the Cardio ward she'd know when someone had their phone on as certain pieces of equipment behaved in an unintended and random manner.