This actually came up in my research. In Peru the highest orchid is always a species of Myrosmodes (formerly part of Aa). These are dwarf plants that grow half buried in high elevation bogs. The normal range is around 4100-4300 m (+/- 12,400-13,000 ft.) with an extreme collected above 4600 m (I don't remember the exact elevation).
There may be some terrestrials in Tibet and environs that get that high up but I haven't checked.