Yes, your reasoning is in line with what I have read.
Distortion was not even on my radar when I started this, but it all makes sense now. I think it may have been nearly unavoidable in this case without pre shaping the tubes. There were a total of 28 welds on the same side of each support tube. Each weld results in expansion while hot and contraction when cooling. During the contraction the steel will overshoot past its original shape. This effect x28 results in what I am seeing...
Interesting but long video on flame straightening that i found useful: