This means there are portions of the girdle that are succeptible to chipping. Sometimes it's not a big deal but more often it is. One good wack on an "very thin" or "extremely thin" girdle and you may be looking at getting it recut and by by 1.5xct size.
Looks like a pretty awesome stone. I don't think I'd be too quick in eliminating it.
The big worry with girdle thickness is "extremely thin". This width has a "knife edge" that chips easily. "Very thin" is considerably safer than "extremely thin".
Also, you might only be dealing with a VERY small segment of the girdle which is "very thin" (usually the case). The rest might all be "medium". If this is the case, any risk is considerably reduced.
Remaining risk (if any) can be essentially reduced to near zero if a savvy setter protects the area with smart positioning.
as Richard says - often there is just one or 2 very thin parts where the orginal crystal was left under the stone. These can easily be set under a prong.
the first stone that started this thread is not all that well proportioned. It would be good to get a more accurate Sarin angle report rather than the rounded %'s and run it on HCA