Two critical parameters for all helicopter are HIGE (hovering in ground effect) and HOGE (hovering out of ground effect). The HIGE and HOGE values for any helicopter depend on many factors, including surplus power, rotor loading, weight, etc. There's another parameter - service ceiling - that may play a factor here. Most helicopters have a service ceiling (commonly defined as the altitude where the max rate of climb is 100 feet per minute). The service ceiling is almost always higher than the HIGE value, which is almost always higher than the HOGE value. The service ceiling is typically higher because the vehicle has forward motion that adds to rotor lift.

Looking at the table in Tom's link, you can see that service ceiling, HOGE, and HIGE values increase as the weight decreases. At a weight of 4960 pounds, the AS350B3 has a ceiling of 14,600 feet, an HOGE of 10,530 feet, and an HIGE of 12,615 feet. Decrease the weight to 3530 pounds and the ceiling, HOGE, and HIGE values are all 20,000 feet. This suggest to me that the 20,000 foot limit is not based on the vehicle's performance but some other factor, such as some regulator or equipment limit.

For this flight, I suspect they stripped out all of the unnecessary equipment like empty seats and unneeded equipment to lower the empty weight considerably below the standard 2603 pounds. My guess is the empty weight was probably on the order of 2300 pounds or so. They took off from a high elevation, probably with a minimal fuel load. Odds are the takeoff weight was well under 3000 pounds. Extrapolating from the performance table, every reduction of 110 pounds raises the HIGE value by roughly 700 feet. That rough extrapolation would give an HIGE of over 25,000 feet at 3000 pounds. There may be another factor - the winds at the top of Everest are seldom calm. That might further increase the rotor lift. Based on the news release, it appears they'd expanded the flight envelop to well over 30,000 feet before attempting this flight. I don't know if they did anything else, like operating the engines beyond normal limits.