Thank you for getting back to me.

But if I am making a Graphic Image and I want it to cover a 4:3 720x480 Video screen.

You say 655x480 is good and then you also say 720x528 is good.

What is 720x528 going to do then if I use 655x480 ?

The video heights (480) are what you should match.
Matching the storage width (720) is not useful because of varying PAR factor.

I said 655x480 is good and 720x528 is good because both are good. Use either one as they both fill the frame.

Just a habit from when bilinear downscaling was thought "good enough" for video.
Even 1 pixel difference would soften the output, so I'll stick with a vertical resolution match as being optimal because it saves a scaling step.

Actually it doesn't. The image will be scaled to 720x480, so any size you use will be rescaled. The advantage of 655x480 and 720x528 is that these two sizes only get scaled in one dimension instead of both. The thing that makes 720x528 more attractive is that it gets downscaled where 655x480 has to be upscaled.

Upscaled to what?
480->480 involves no vertical scaling whatsoever.
I ran the tests when I was comparing Vegas 2 to Pinnacle.
I->O is pixel for pixel.
That was over a dozen years ago.

655 -> 720 is upscaling. True, it's horizontal, not vertical, but it's still upscaling.

I was extremely careful to speak to vertical resolution only, because for humans, that is the most important perceptually,

Since you mention it, your example is not horizontal upscaling BY DEFINITION, since Display Resolution (scale) is unchanged.
It is horizontal resampling, which must always take place at some point with anamorphic source. The distinction is important, because the implications of resampling alone wrt detail are relatively insignificant compared to rescaling.

While most home playback will handle anamorphic through player resampling, all web delivery needs 1:1 PAR, so encoder resampling is necessary. In doing this, deliberate rescaling of vertical resolution is unnecessary at best, and I never recommend it because it adds a redundant step.

To close, I'll repeat that the inevitable horizontal resampling of anamorphic source is not scaling, simply because the scale does not change. Vertical rescaling (up or down) should be avoided if at all possible for optimal retention of already-fragile detail in SD source. Hope you're off to a great spring!

I seem to be sensing this a lot lately:
"If we only talk about it long enough, musicvid will run some tests."

(Probably not the best way to demoire . . .)
[cough]