The photo would presumably give a date/timestamp of when it was taken. Theoretically if someone set forward the date/time on their phone by a week then I would think that is the date that the photo taken today would show. The date/time on the phone could then be reset to be being correct and the photo would appear to be from the future.
However, if the police them looked at that photo next week, it might say it (EXIF data) was taken 'today' although the file will show it was created a week ago. So if someone wanted to fake it my opinion is that they would set the date forward on their phone and take the photo to get the EXIF data. Then remove that photo from their phone (bonus points for wiping the phone so no data is recoverable that there ever was a photo taken then) and store on a usb drive or similar. Then on the date you wanted to plant the photo, copy it back to the phone (ideally at as closet to the EXIF data says it was captured as possible)
Then again, I am sure there is software to change the EXIF data, date created properties etc which is probably easier to use than the method I described above
So while I don't think the photo is not real, I also don't think it is beyond the realm of possibility that someone could manipulate the timestamp/EXIF data and the police would be none the wiser.