Can car alarm be set off by cell phone?

["DanK" <djk104@xxxxxxxxxxx>]

We have a 2004 Toyota with a factory installed car alarm.  The alarm
goes off randomly.  Sometimes a few times a day, some days not at all.
No physical disturbance is setting it off (it does it even sitting in
our closed garage).  However, we noticed that it seems to happen when
my daughter's cell phone is in the car.  I am still trying to confirm
this relationship (by having the phone in there, or not having it in
there, and seeing when the alarm goes off).

Could the cell phone be setting off the alarm?  It's nothing obvious,
like the phone being on "vibrate" mode, and receiving a call.  Could
the phone be sending a radio signal that is at a frequency that sets
off the alarm (like the frequency of the emergency button on the key
pad)?

We had it at the Toyota dealer, but they didn't find anything (this was
before I made the cellphone connection).

Thanks for any help!

DanK