[franken]

Right. Think of the tank as a battery. The alternator won't provide the current needed to start the car. Yes, compressor makers lie. That's why you buy from a reputable seller and not Lowes or Home Depot.
Any 25 gallon compressor pretty much has minimal capacity to do anything but make someone newly married blow some crap out of the garage and impress the husband or wife.
If the pump has the capacity (which they never do) to provide the needed pressure and CFM, all is well.
HVLP means high volume low pressure. A 25 gallon compressor can't provide the volume needed to paint much without rest to refill the volume of air in the tank.
Yes, good Milton fittings throughout will help.
As I said, you can never have enough air...