I have looked at the thread you linked. I don't have any particular knowledge of this test, just what I read on the Myhill website.
The 26% blockage of active sites refers to blockage of active sites in the electron transport chain, according to the test, by benzoate and nickel. The enzyme complexes in this chain transfer electrons produced from oxidation of NADH and succinate from the Kreb's cycle, to oxygen, through a series of redox reactions. The energy released is transferred to ATP synthetase and ATP is generated. This is the main, but not only, source of ATP to power the cell.
So the blockage is not in the Kreb's cycle as such, but downstream in linked oxidative phosphorylation reactions. The effect is to reduce production of ATP.
The second part of your question relates to a possible link between benzoate as the blocking agent and acute hyperoxaluria. I think you are asking would benzoate ingestion cause acute hyperoxaluria and if so, would blocking of ATP production be the mechanism?
Please correct me if I have misunderstood you.
I can't think of a way that this could happen and in fact, googling benzoate and hyperoxaluria shows that benzoate administration has been used to try to reduce hyperoxaluria. The reasoning was that benzoate traps glycine (forming hippurate) and since there is some evidence that glycine is transformed into oxalate, this might be a way of reducing it.
The treatment was only slightly successful for a short time, presumably because we now know that glycine makes only a small contribution to oxalate formation. Personally I think this shows poor understanding of the central role of AGxT (alanine glyoxylate aminotransferase) in controlling oxalate formation, though these seem to be very old studies and maybe less was known about the enzyme then.
Setting benzoate aside, I can't see either how reduction in ATP production would precipitate acute hyperoxaluria. I can think of how the opposite could happen, ie hyperoxaluria could reduce ATP production.
The only other link that I can think of, though this is sheer speculation on my part and I don't know exactly how it would work, is through sulfation pathways. Benzoate is a phenolic compound, of the type that causes salicylate sensitivity. This is thought to reflect problems in the phenol-sulfur transferase pathway, possibly a shortage of usable sulfate ions.
Salicylate accumulation can overwhelm the pathway, in effect paralysing it. Possibly a decent dose of benzoate could do this.
Oxalate is transported out of the body in exchange for sulfate, so shortage of sulfate can also be a problem here, but maybe if sulfate use elsewhere were paralysed, an increase in sulfate availability might stimulate the transporter to dump oxalate.
