Well from the little I know about welding (close to nothing) and
what I know about physics (fits in a hand)
I tend to say both statements are true somehow.
And here's my explanation for this:
heating steel without proper tempering
makes it very brittle too meaning it breaks before it bends.
[edited.. thanks DaiSan]
The weld joint is different, different material, different material thickness and very different way of bringing metal into a form.
thus chances are that a good weld will be stronger than it's surrounding metal.
(not the original metal though)
But in fact it's not better than a good bend.
Although a bend weakens metal too
-most bends around here are cold pulls so the outer wallthickness will decrease-
the fact that the metal wasn't heated the part kept it's original flexibility.
And flexing is what you need in a unsuspended kart,
that's not an issue of comfort, but of preventing the kart from falling apart.
The times I've seen people breaking welds, the metal will give away before the weld true, but always directly NEXT TO the weld,
and the reason for that is the welding, not the weakness of the material as such.
I guess if you temper your frame after you're done
the weld if filed down to the exact same thickness as your original material will be the weakest spot.
[edt again

]
lower on carbon.. perhaps (not necessarily though) but that doesn't help anything after all the heat
Try this at home:
get a welding wire cut it in two, join it with a weld spot, let it sit on your bench to cool
file it down again and try to break it.. (don't cheat

)
Now repeat but anneal it first.
See what happens
Feline, allow me to say a few more words...
The first thing I saw one of your posts, you stated that you and your dad with a combined knowledge of 50something years of being a machinist
couldn't figure out a way to stick a 1" axle through a 1.5" hole...
just to find out that the part to do that properly is already available
for at least 20 of said 50 years.
The second time one of your posts sticked to my mind is
when you say a Honda GX (not a clone, but the real deal) is crap.
Which can be considered as blasphemy,
at least it's the most uneducated opinion I've heard in a while
And now your statement again is at least arguable;
as it contradicts nearly everything
bike, kart and car builders do for a lot more than 5 decades.
In the end, I'd say you chose your usertitle wrong...
it should say "
Death by misinformation"
'sid
[
EDIT]
I edited this post after the clarification from DaiSan below.