When I lived in the US, I found people were very informal with respect to their handicap indexes and what was submitted. It was kind of annoying. While the system in Argentina is certainly not perfect, if players sign in all medal play rounds as they are supposed to, handicaps are quite accurate. Only tournament scores are accepted and tournaments are played most week ends at most clubs, as well as some week days. The Committee can adjust course rating if conditions are difficult on any particular day. The only way to artificially inflate a score is to purposely play badly in tournaments for some time, and given that the system only considers the 8 best rounds out of the last 16, this is tough to do.
Anyway, as I understand it, most of the major governing bodies around the world are working on a universal handicap system that is considering the best of several systems. Could be interesting to have a global handicap for the first time.
As to courses with no defined set of tees, this week I toured a brand new private course in Argentina with one of the most respected contributors to this site. It has 9 greens, and several dozen formal teeing areas allowing for play into each green from multiple directions, and of course multiple routings. The teeing areas can be set up with tee markers, but they are often left with no markers allowing for free play. Of course this is made easier because only 8 people are on the course at a given time.