OK. Now I believe you, Kits and Jim. I had to read up on plant
physiology in order to understand why this might be true. Anyone who
has the requisite fortitude can read this:
http://web.ics.purdue.edu/~tuy/thesis/Review.htm
but everyone else is welcome to my summary:

Flowering is very complicated, influenced by hormones and climate.
However, there is one simple fact: there is a short period in summer
when the new branches have finished elongating and developing buds
"decide" whether to include flower primordia or not. Now I had assumed
that the decision would have been made based on plant health: A healthy
plant would have the sugar supplies to invest in flower buds. And this
is roughly true. A tree that is very drought-stressed will not put
energy into next year's flowers. A tree that has been defoliated will
not flower the next year. However, a healthy tree that has flowered
heavily that spring and set a lot of fruit will not form as many flower
buds that summer because all the spare energy will be going to the
currently-developing fruits. It's not "health" per se that decides
flowering (plants don't have nervous systems; they don't "know" if they
are healthy or not), it's sugar. The buds will develop flower
primordia if sugar is present. So in what situation would a tree be
dying, yet have lots of sugar available? Easy: if the roots are
rotted. Roots are generally the sugar storage site: if the root system
is inadequate due to stem girdling, root pruning, or root rot, the
extra sugar will be available to stimulate flower bud formation, even
though the tree is in danger of dying.

Nina, now satisfied.