I don't know that's what happened, but it's certainly plausible. If it is, it speaks well for Kelly's powers of observation (noticing that the phone was behaving in an unusual way) and ability to choose a proper course of action (taking it to the security professionals at the White House, rather than, as someone else noted, Geek Squad or whatever minimum wage clerk was manning the counter at the Verizon store).
How about any number of several dozen extremely obvious possibilities. A family photo album is on the personal phone and he wanted to retrieve it, so he used the phone and noticed something was wrong with it. He needed to retrieve contact information for a friend that was stored on it. You know, the same exact reasons any of us might fire up an old phone we still have.
I've added an edit to provide the clarity that should've been there initially.