Joker chase, Batman, "Flip a big rig"

The details are available in detail on the Batman Dark Knight DVD.

Yes, they did that for real, twice actually as they had flipped a truck earlier to show it could be done. The technique was simple, they just put a huge air-ram in the trailer and fired it. The ram itself was digitally removed in post-production, but if you watch the scene again you may notice the clouds of smoke emanating from the trailer as it is flipping. That is the air that came out with the ram.

It was filmed in the business district of a major city, I forget which one, in one take at night.

I know that the driver was secured with webbing that would make spiderman turn green with envy. But beyond that (and one assumes some major reinforcement of the cab) I don't recall them mentioning any alterations beyond the fitting of the ram. I can't see them welding the trailer and cab together if only because they would never have been able to get it around corners to get to the filming location. But it is possible they designed a simple rig to keep them together. If so this isn't mentioned in the mini-documentary as to how they did the stunt.

I'm unsure what MB think of this myth. They have certainly heard of it, given that its something that has been posted continually since the film came out. But they've already done two myths, the Batmobile cable turn and the Hellboy car flip, that would tell them that A; No cable is strong enough to stop anything close to that size. B; Even if the cable didn't snap you are not flipping a truck, or a car for that matter, with force applied to the front bumper. So they might not find it all that interesting to do.
On the other hand if they wanted to do another supersized special this might be something they might feel is worth doing. It would be fairly straightforward, not least because duplicating the results would probably involve little more than calling up the guys who did the stunt and asking them for details on their rig.
Then again, while it might be simple it would require a lot of work, none of which could be carried out at M5 as they don't have the room for a truck that size and the modifications needed are not something they could do on location.