So lets say your SAE numbers are higher than your uncorrected(actual) numbers, could you still rightfully say the SAE numbers are legitimate power of the car?
Not really, although that is the goal, the problem is the dynos weather station is not that accurate and can be fooled, intentionally or otherwise.
The purpose of SAE correction as others have stated is to "normalize" the environmental conditions. The older SAE J607 standard assumes the engine is being run where the environmental conditions are 60F, 0% humidity with a barometric pressure of 29.92 in-Hg. Whereas the newer SAE J1349 standard is 77F with 0% humidity and a barometric pressure of 29.234 in-Hg.
That means if you were to place your car in an environmentally controlled room having those conditions, the SAE corrected H.P. is what it should make. Therefore, you can take two cars for example; anywhere in the world at any time and compare their SAE corrected numbers as though they were being tested in that same room at the same time under the same conditions. "Same conditions" meaning using the same SAE standards: either the J607 or J1349. You can't compare apples to oranges.
Again, it's a great idea in theory but in actual practice, it is not that accurate a lot of the time for a variety of reasons.
I should add that the LS7 for example was tested using the SAE J1349 standard. So, if the current weather conditions are better or worse than that the engines performance will be either > or < than 505 H.P..
Given that, is the engine a 480 H.P. engine or a 530 H.P. engine? Again, it depends on the actual conditions. The 505 H.P. was achieved under those specific conditions and since all LS7 engines are virtually identical, they all test the same, under the same identical conditions.