From my experience, the "H" tapes are usually the corrected version. Usually.
I believe I have in my pile a Jim Croce tape that has an H, but still has a channel placement error. More often than not, it's the "C" tapes that have the channel error, and 9 times out of 10 you've got to swap Front Right with Back Left.
Here's my theory as to why:
If you notice on this Three Dog Night Quad Master, the channel layout is listed as:
Track 1: LF
Track 2: LR
Track 3: RF
Track 4: RR
Which is great if you want to cut channel crosstalk to a minimum. This is standard industry practice too! Even on the lowly stereo 8-track tape, the tracks for program 1 are physical Tracks 1 and 5; as far away from each other as physically possible with the head layout.
So, if the duplication engineer is paying attention, he would map out the tapes channels accordingly. But if he's not paying attention, we get:
Left Front in it's correct spot.
Right Front in Back Left
Left Back in Right Front
Right Back in it's correct spot.
I've yet to see any other ABC/GRT 4-channel Master tapes, so I can't say this was how all the masters were labelled when they went for duplication. I still think this one is the smoking gun as to why some tapes came out the way they did. Unusual in the fact that 'Coming Down Your Way' is one of the tapes that does NOT have a channel error.
JonUrban had a point that perhaps the C/H controversy is more to do with a price point as opposed to mixing. He could have a point with that. C versions, being the initial releases at the lower price. H versions being released later at a higher price, but also being duplicated with correct channel assignments. I'm sure people complained about this back in the day!