It's definitely because the files are corrupt. Photoshop can't read the file because it encounters the end of the file on the disk before the place where the file header says is the end.
If you remove your SD card from your PC without using the 'eject media' function you can corrupt the files on the SD. I do that all the time, but about 99% of the time, no problems occur. If you copied them from a corrupted SD to somewhere else, they may copy but still be corrupted.
As far as ones downloaded from the Internet, either you copied them to the SD and then moved them back or you have some bad corruption on your hard drive.
Take a SD and format it. Do not use 'quick format'. Copy some known good files to it and then back to your HD. See if you can open them in PS. If so, the SD is probably ok. It may be that your camera's formatting and Windows are 100% compatible. This is especially true on older Camera cards.