Working in the mobile industry, I can say it does happen. There are phantom ring tones, but they certainly are not common. I've seen situations where a telco will hand a call to another telco (much like internet routing, there are often a lot of carriers between you and the person you're calling). There are scams some dodgy carriers use where they play a fake call progress tone (ie, the ring tone you hear) and it's not actually a ring tone. They connect the call on their network and play a fake tone, so you think it's ringing but they're collecting revenue for terminating the call.
That's probably around .005% of calls that that may happen to, and i've not seen it in quite a few years (often it's actually calls from o/s to AU mobiles that are the worst due to the high cost of terminating to AU mobiles).
If the calls were ringing and no answer, this can be very very easily investigated. Calls have CDR's (call detail record) which has all kinds of information. Telcos can do this easily (i've done it a bunch of times for fault finding). It doesn't show where the customer was, but it's easy enough to see when a mobile is roaming onto a foreign network, what country the phone was connected to (and, in most cases, the exact carrier they were roaming on).
The telco world is anything but simple, but to say 'oh it often happens' is flippantly dismissing it IMHO.
And due to the way radio waves propagate out from the base stations, they would effectively have to be aimed at the sky, or at an angle that would allow them to travel and intercept the aircraft (as jb says, it is only for a matter of seconds typically). Of course, if the phones landed on the ground.... (i'll not add fuel to conspiracies though).
, still powered up, must be phoning home.
