Not to imply that it can just be done easily to every phone, or without preparation or perhaps previous physical access, but this concept has come up more than once in the mainstream news in recent years. So this level of incredulity seems misplaced.

http://www.slate.com/blogs/future_tense/2013/07/22/nsa_can_r...

https://www.tomsguide.com/us/nsa-remotely-turn-on-phones,new...

Honestly, I thought it was a well known thing by now. A quick search on google turns up multiple writeups.

> "Can anyone turn it on remotely if it's off?" Williams asked Snowden, referring to the "burner" smartphone Williams used for travel to Russia. "Can they turn on apps? Did anyone know or care that I Googled the final score of the Rangers-Canadiens game last night because I was traveling here?"

> "I would say yes to all of those," Snowden replied. "They can absolutely turn them on with the power turned off to the device."