Yup, you're right it can be modified but then the file properties would show that too because the file modified time/date would differ from the modified exif data showing when the photo was taken. Technically both file create property and exif metadata should match as the capture time is the same time as the image file being written to storage.
Basically every photo taken with a digital camera has two areas for properties, the basic file data itself which every file for anything has, which among other things includes Date Created and Date Modified, and for photos, EXIF data which includes the original date taken (assuming the date and time on the camera were set correctly) along with GPS data if available and exposure settings/copyright info etc etc.
The three Date related properties between file properties and EXIF should match up. Some metadata can be modified after the fact, but there would ve signs of modification when looking at the metadata in detail generally.
Would it not be possible to circumvent a lot of this by changing the system time on the computer you are using to edit the file?