Do not sit the Restrepia in water. Sitting epiphytic orchids in water will rot the roots out over a period of time. They are not bog plants, even though they appear to be grown like one in cultivation. They grow on trees in mid-elevation, moderately cool, evenly moist (not wet), tropical rainforests in the wild.
The temperature range they grow in is typically 12.8 C - 32.2 C (55 F - 90 F).
Humidity of 60% - 70% is fine, although they can handle it much higher than this range. If they are grown far more humid, you must water less.
The amount of light they should receive is typically bright shade to moderately bright indirect light.
Here are links to how they grow in the wild:
IMG_1383 Restrepia species in situ at Ecuagenera Reserve - Ecuador - Ecuagenera Orchid Tour | Flickr - Photo Sharing!
Restrepia contorta | Flickr - Photo Sharing!
Aside from moss, they can even grow in small grade wood chips quite well. Growing in CHC will work too, but watering schedules will have to be adjusted.
Yes, their roots are thin, and that is natural. Just as many other orchids that grow on trees, (orchids that grow on trees are called epiphytes), the roots can photosynthesize when exposed to a light source. Many epiphytic orchids have chlorophyll pigments in their roots.
Note: The word epiphyte translates into -
"epi" = surface
+
"phyte" = plant