I think we agree: 1/4" is not much, but it is a little (so not 0).
"the top, with the old integral bar removed, sat flush on all six blocks without tension": so without load the bottom edge of the top was flat, or at least conforming to some consistent shape.
"With the new bar fitted the top sat 1/4" above the C-bouts while flush with the top and bottom blocks." So installing the BB pushed the centre up by 1/4". Hence the BB was sprung, and probably by more than 6mm (my 6mm are between the ends of the BB and the top, before glueing, but that gives clearly less than 6mm deformation, as both BB & top bend, and meet somewhere in the middle, when joined).
Then pushing-down the centre to make the top fit at the C-bouts increases the load towards the ends of the BB and, over time, might encourage a fig.3-like deformation, referring to Mr. Bollbach's story. I say 'might' as it is by no means certain to happen. What happens over time depends on the arching (relief, both directions are important here), wood quality, graduation, ..., . In a situation like figure 4, some (= 'a little') load by the ends of the BB may be carried well by the arching near those ends, and will not lead to deformation on the long term, but instead helps to enhance the top's carrying capacity a little. Furthermore, some pre-load from the BB will enhance a gentle arch in the top, in the middle section (right where the bridge sits & where the BB is deepest), further enhancing the carrying capacity (well, unless you push that bend back of course).
Yes, once again, there are far stronger pre-sprung bars around, and the pre-springing does not really help but instead can give substantial problems.
Carrying capacity comes from the geometry, not from elastic forces in a bar. Yet some judicious elastic pre-load can help a little, depending on circumstances. (IMHO, YMMV, ..)