Is their 'shelf-life' indefinite?
No. They last about 5 years or so, depending on what temperature they are stored at.
For all intents and purposes. They will be good for years if kept cool and dry.
They are no longer freeze dried. I got out of the Marine Corps in 89 so everything is different, The freeze dried ones were practically forever. but there are people who have eaten (the new kind) 10 y.o. MRE's without issue. As long as the package isn't swollen you should be okay out to 5 years at least.