Actually, I doubt their claims to copyright would stand up since the flag itself is owned by the country in question, not the person who made the image. But their are free sources of flags as well, so the point is moot.
Another source of the flags would be the
CIA World Factbook, which is public domain. The only issue with using the flags there is you would need to resize them if you want them smaller.
A lot of these other sites claiming copyright to the flags simply stole them from the CIA World Factbook or other sites, and then claimed they created them simply because they resized them. Usually it's just a tactic to get links back to their website and they have no real legal standing... especially when they are simply posting a resized public domain image they are claiming is their own.