Yeah, we did not have a section for shoes here, because this is a Barefoot Running/Walking forum, and there are millions of places on the internet (most paid for by shoe companies) where you can read about footwear...
That said, now there is a section.
However, I have little experience with the Invisible Shoes, I just can't see them.. ha, ha,... nor do I frequently use any other minimalist footwear for that matter. I do have some ninja shoes/socks which I can carry in a fanny pack, and I keep flip-flops in my car(s) for when I want to avoid being harassed or stepping in muck on restroom floors, especially when I'm traveling which is already stressful enough in itself.
But seriously, my requirements for footwear are that they either help me move faster and/or more efficiently (ie: roller blades, skis, rocket boots, etc.), and/or (because I certainly don't want to wear footwear all the time) that they are at least easy to remove.
Anything that is time-consuming to remove or put-on is going to discourage you from going barefoot whenever practical (short breaks from work or school, walking from your workplace to your car, etc.). In other words, if it's easier to just leave the shoes on your feet, rather than remove them (kick them off) when you have an opportunity to go barefoot for a few minutes, then that would be the wrong shoes for me...
As far as claims made, and whether their "true" or not, you'll find little research has been done (and it will need to be long-term research when it is done).
However, we have seen on our Yahoo! forum http://sports.groups.yahoo.com/group/RunningBarefoot/ many people claim that their toes spread out more, they developed arches, and of course the foot becomes stronger (after all, it is being exercised more, once you lose the supportive shoes), when they go barefoot more often.
There is little data, as these are things reported in real-life, not in research labs, though there have been some studies of people in societies where they never wear shoes, and they simply don't have most of the foot problems that are common in our society where people where shoes most of the day. See http://www.stevenrobbinsmd.com/ for more info.