In rec.crafts.metalworking Ernie Leimkuhler wrote:

If you TIG weld 4130 using a ER80S-B2 filler rod, no post weld heat
treat is needed.

Read this page
This guy works as a subcontractor for Northrup's Skunkworks.
He knows his ****, and teaches airframe repair classes across the
country.

http://www.tigdepot.com/faq.html

Actually what I was wondering about post-weld stress relieving using a
torch (which the author of the above link says is required) and not heat
treating/annealing, but thank you for the link and the information. It
seems like Finch's text is the only one that flat out says that post-weld
stress relieving isn't doable... it also says that the heat treating isn't
necessary either, but then the only book I've seen that says you do need
to do it is in some by Carroll Smith, and he talks of it more in terms of
actually treating the part to a certain level of hardness to attain the
required mechanical properties for a part's design, which seems valid.
I'm sure for his designs and applications he knows exactly what he's
doing, and probably has the real world examples to back it up.

I guess I'm still no closer to a real documented answer to the question,
unless I can find some actual stress analysis studies of stress relieved
joints versus non-stress relieved joints. In the meantime I suppose it's
best to simply follow what the majority of experienced folks do, since
they very likely have good reasons for doing it the way they do.