That youtube video has some inaccurate and confusing information. Any system or feature that bleeds air off the engine is an "engine bleed air" system or feature. There are stability bleed ports and valves, and there are aircraft service bleed ports and valves. The system affected by the AD is the aircraft service bleed air that comes from the engine from either the 9th stage or 5th stage of the HP compressor, depending on the source pressure. It's the system that feeds the air conditioning packs (pressurizing the airplane) and the wing anti-ice system. It is not an engine stability bleed or starting bleed valve. The 5th stage check valve on the affected airplanes is not spring-closed. It normally moves to the closed position due to gravity and air flow/pressure. When the check valve sticks open it's not the 5th through 9th stages that stall - it's the stages downstream of that area that stall initially, leading to compressor flow reversal (the "bangs" you hear about in the reports).
But yes, if it sticks open you will almost always end up with a shutdown, and if it sticks on both engines it's likely to be a forced landing. The AD was issued because the first few flights after a storage period have a risk of dual engine shutdown that is quite high.