Here's an example of the kind of moron who believes this sort of stuff
So here we have some of the most broken, retarded logic I've ever heard. "It can't be an AM radio - they didn't exist back then!" Guess what dickhead,
cellphones didn't exist back then, why not apply that perfectly reasonable logic to them? "I'm stumped, I can't explain it, you can't explain it - it has to be a cell phone" This kind of argument is used frequently when trying to convince people of the supernatural and it basically boils down to "I can't exaplin it, therefore I can explain it." I can't explain why the door slammed, therefore it was a ghost.
There are about 10,000 more probable explainations than it being a time travelling woman who went to the trouble to dress herself in period clothes to avoid detection, but then walks down the street openly using non-existent technology, with no-one batting an eyelid. Firstly almost all of the 'proof' is suggested rather than clearly evident in the film - she's talking, she's holding a phone to her ear etc (Even after saying I'm going to let you decide for yourself he tells you what you're seeing). She could be scratching her face and talking to someone off camera. She could be holding a poultice or ice pack to her mouth and her mouth is open because she has toothache. She could be using a 1920s hearing aid, which looked like this...
And setting the volume by talking, as people still do nowadays with hearing aids.