I don't doubt the chart. Yet I want to know "why". Here's what doesn't seem right. Atmospheric pressure doesn't only push "down" it pushes outward in all directions.
You have to look at what forces are on the oil in the sump that will move the oil to the pump inlet when the pump is turning and the inlet is at a lower pressure (suction/vacuum) than the pressure on the oil at the pick-up. Fluid always moves from high to low pressure (delta-p). The pump inlet chamber will be at some level of vacuum depending on the exact pump design, health and its rotation speed ... and that holds true regardless of what the pump outlet is doing - it's the beauty of a PD pump. On an ideal PD pump, the inlet side will not be effected by the outlet. A PD pump that is producing 100s of PSI on the outlet (depending on what it's connected to) will still produce the same essential vacuum/suction on the inlet. The force on the oil in the sump is the only thing that moves the oil into the pump pick-up tube and into the pump. Imagine if you could pressurize just the oil sump volume (but not the rest of the engine's volume) to 65 PSI of air pressure (50 PSI above ATM). Pressurizing the sump would help push that oil more effectively through the pick-up tube to the inlet of the pump which would still be at the same vacuum level even though the outlet is at high pressure. If the oil became thick enough, and/or the driving force of the oil low enough (near zero air pressure for example), then the flow going into the pump will become less than what the pump is capable of moving. When the pump starts getting starved of inlet volume, then this is when pumpability issues begin.
This is also true for the W rating pumpability viscosity defined in SAE J300. At some point, the cold oil's viscosity is just too thick for the forces on the oil in the sump to move it effectively to the pump. If the oil is very slow to get to, or can't get to the pump at all through the pick-up, then there will pumpability problems and lack of lubrication to the engine. Cavitation will most likely be going on too, which hurts pumpability and could also cause damage to the pump itself.
Now imagine a bucket full of a fluid like water or oil.
If atmospheric pressure pushed "down" on the fluid then it would weigh more at high pressure and less at low pressure. But atmospheric pressure doesn't affect its weight. It weighs the same as ambient pressure rises and falls.
If you had a super accurate scale that could measure down to a very low weight increment, the bucket would actually weight less if all the air above the oil was removed (ie, a vacuum) from the system, because air does have weight. The air pressure on everything on Earth is due to the total head pressure of the thickness of the whole atmosphere (60 miles thick) surrounding Earth. If you could slice out all the air above the bucket 60 miles high and weigh it, it would weight quite a bit. But since the bucket is completely surrounded by air, the pressures cancel out. Maybe this concept is what you're locking onto which might be confusing the issue when talking about PD pump operation (?). Imagine what the bucket would weigh if you could somehow remove all the air just located below the bucket but still have 14.7 PSI pushing down on it. Do the calculation - ie, 60 miles of air head pressure, which would be 14.7 PSI pushing down with no reactive force on the bottom of the bucket ... it's surprising.
Now poke a hole in the side of the bucket near the bottom. The rate at which the fluid drains through the hole does not depend on ambient atmospheric pressure. Ambient pressure pushes down on the fluid in the bucket, and also pushes in from outside the hole, equally. No net effect or impact on the rate of drain. It drains at the same rate regardless of ambient air pressure.
If your example is an open bucket, then yeah the ATM pressure won't matter because the force on the water is ATM pressure + head (gravity), and the hole outlet is going to ATM. So only the head pressure of the water depth is the driving force to move the water out the hole in the side. But a PD pump does not work that way.
Now say the bucket is an engine oil sump and connect the hole to a PD oil pump. If lower air pressure didn't slow down the drain rate through the hole, how can it affect the intake of the pump?
A PD oil pump is not like an open bucket with a hole in the side. In your bucket example, there is no additional delta-p between the water on one side of the hole and the ATM beyond just the head pressure of the water.
The inlet of a PD does not operate at the same pressure level as the outlet ... far from that. The inlet of the PD operates basically at vacuum (suction) dependent on it's design and RPM (regardless of what the pressure on the pump outlet is) which makes the delta-p between the oil in the sump and the pump inlet greater than what's going on in your bucket example. The greater the delta-p, the greater the driving force to move the oil from the sump to the pump inlet. If you could magically remove all the air pressure on the oil in the sump and only left the head pressure from gravity, the driving force would go way down, and if the oil was cold/thick enough it would start impacting the oil flow through the pick-up tube and into the inlet side of the pump. At some point pumpability would be effected. If you could then magically increase the pressure on the oil that's pushing it into the pump inlet (all other factors held constant), then that same thick oil would move better to the pump inlet. It's the pumpability of the oil for that specific pump, which can be effected by a many factors - and the ATM pressure due to elevation is one of those factors.