Phisherman wrote:

I hear that walnut is toxic all the time. Yet, my parents had 70-foot
walnut trees in the backyard and grew all sorts of flowers and
vegetables under them. However, the trees are messy and the fruit
stained the concrete patio. I heard that walnut sawdust should not be
used in horse stables.
....

It depends on what, in particular and also on particular soil pH, etc.
as to the extent of the effect. Foilage on bulbs, in particular, are
likely to show signs...it's not so strong and effect as to be deadly to
virtually any plant, but in general, a comparative specie outside the
influence of the walnut will typically show better development than one
within that influence. I'd not use it in veggie gardens simply as a
precaution against poor germination, etc., not that I'd be concerned w/
human toxicity, etc. I also made the recommendation in context of the
OP in this thread asking about using fresh sawdust directly...