Very observant of your friend! Lucky for us, we don't need to maintain the exact environment that most corals live in to be able to keep them successfully.
Pressure doesn't seem to be an issue for corals, as many of the animals that we keep are found in rather shallow water, typically the top 60' of the water column. That's where most of the light is. Also, since corals are sessile, they don't have swim bladders like fish do, so aren't as susceptible to pressure changes.
On the surface we are subjected to 1 Atmosphere (ATM) of pressure from 18K ft of air above us. For every 33ft you descend underwater, you increase pressure by 1 ATM. That means that most coral specimens are found from 1 - 2.5 ATM.
Given the success of many corals in fairly shallow reef tanks, it appears that pressure is not a requirement for survival. Add to that the fact that most coral species can be found at varying depths in the ocean, though many have a preferred range.
A better question might be, what effect does altitude have on keeping aquariums and their inhabitants? That is also directly related to pressure.
At sea level, disolved oxygen (DO) reaches 100% saturation in air at 8.6mg/l. Water holds less DO than air, saltwater holds less DO than freshwater and as altitude increases, DO decreases. DO also decreases as temperature rises.
The following is an example of DO and temp, salinity and altitude for 100% saturation:
25c (77F) 0ppt = 8.26 mg/l O2, 36ppt = 6.72 mg/l O2, 36ppt + 5400ft = 5.5 mg/l O2
30c (86F) 0ppt = 7.56 mg/l O2, 36ppt = 6.20 mg/l O2, 36ppt + 5400ft = 5.0 mg/l O2
0ppt = Freshwater 36ppt = Saltwater
Most fish will start to succumb to O2 starvation around 4 mg/l, though some will survive at lower levels. High activity fish such as tangs and anthias have a higher DO requirements.
This is why a loss of power at our altitude can result in the loss of many of our tank inhabitants. Falling temperatures actually benefit this situation, but the most common mistake new folks make is to allow the heaters to come back on when the power does.
Summer also presents a problem for us. Tanks that reach upwards of 90F are certain to experience problems due to low DO levels.
Heavily planted tanks, or tanks with lots of Cheato in their refugium also need to watch DO levels. When the lights go off, plants take up O2, just as the fish do. By running the refugium light cycle opposite from the tank light cycle, you eliminate the likelihood for low DO levels.
Dissolved nutrients also reduce the DO level of the water. So high nitrate and phosphate levels, while bad for your corals, also reduce the DO level of the tank.
With all of that having been said, how in the world do we manage to keep critters alive in our tanks way up here? We supersaturate the water through the use of skimmers, surface agitation and increased flow. Regardless, we can't replicate the DO found in natural seawater.
What can we do to help increase DO? Run your tanks at cooler temperatures. Your fish and corals will be quite happy at 76F. Many animals will do well at even lower temperatures; research your animals. If a fish only aquarium, consider reducing the salinity for heavily stocked tanks. This is NOT a solution for reef tanks.
Pressure is a concern..... but for us, it's actually the lack of pressure!