@ tommoutrie...
Your question is very valid...
I do not believe the aircraft manufacturers are lying about their performance data but they sure make it very hard to go through the charts and get a figure without making a mistake.
When you buy any aircraft today, you ought to be able to with some sort of software to get the "correct/approved" AFM numbers.
This "software", an electronic version of the approved AFM performance chapter should be given to the operator as part of the purchase of the aircraft.
Now even if you come up with the "correct" numbers it is in no way giving you the appropriate airport analysis so you still need to go to an outside source for that like APG.
APG or any other supplier of airport analysis will come up with numbers that meet the minimum standard to clear an obstacle in their procedure and yes those are very small margins.
It is up to you to decide if you want to get the most out of the analysis or back off a notch and use a safer number (higher OAT or less weight) to give you an additional buffer.
The airlines to it the same way, there is no magic in their procedures. I have seen American Airlines leave people and baggage behind at Eagle for flights to Chicago and this with a B757.
FYI, in Eagle our ops with the CL604 for takeoff was day basically VFR (5000' - 3 miles) and load up the aircraft (pax and fuel) to meet the climb gradient required to clear the obstacles for a given OAT.
Note: You could not factor in engine or engine and wing anti icing into the numbers unless you planned to stop in Denver.
For landing, especially at night, if you did not see the airport while on the LOC at 10 miles final you were not to land there, no circling is permitted.