Thanks to all of the suggestions above, I dug out the set again and did various tests.
The tender does NOT derail when no car is attached.
The rear truck of the tender seems to swivel the entire left-right path that it is allowed to (the body of the tender stops it from "over" rotating.
Here's what I found out that is really the culprit:
If a trailing car's link coupler is coupled to the LEFT of the tender's links, the tender's rear truck derails going around RIGHT turns.
If a trailing car's link coupler is coupled to the RIGHT of the tender's links, the tender's rear truck derails going around LEFT turns.
It's as though the link of the car pushes the tender's coupler too far out of range forcing the wheels to derail.
I tried the test with 4 different cars attached to the tender and got the same result no matter which car I used.
This is really a sad statement on the construction of these link couplers. The train can't run on the curves included with the set!!!!!!!!!!!!!!! How sad is that?!
I'm now thinking that TinplateBob's solution may or may not solve this problem. I would say that it would if the car's link pushed on the tender's link but that's not the case. The car's link pushes on the tender's box itself.
I have had nothing but bad experiences since I entered the tin-plate world last October. I'm really regretting now selling off my entire collection to make this transition.
Sorry about the moaning but some may understand the frustration.