99% of home garage doors have a manual cable release which detaches the pulley from the chain drive and allows you to manually open the door... I'm surprised people wouldn't know this especially in Texas
and 99% of garage door owners probably don't realize there's a counter-balancing spring "right there!" making it easy
The release is inside of the garage, so unless you have the key (not as common as you'd think) you're out of luck.
Also I'm sure it'd get annoying to manually open the garage all the time, especially since this article seems to imply that the phenomenon lasted for a while
If you have a garage door opener button that is not working, you likely have a key to get into the house enter the garage and manually open the door.
I do not think that we are to take from the article that these home owners left their cars inside their garages until the NSA changed their frequencies. I understood that for a while they were interrupted in what they were planning to do.