I wouldn't call it a long shot at all. The diagnosis is correct, though it might be hard to figure out where exactly that track/joint is.
The issue can be triggered by motors in two ways:
1. interference on the power line (by either too high resistance on a power path, or by lack of filtering capacitors and power fluctuations caused by motors)
2. by a cold joint/broken track, which normally works well enough, but with vibrations from motors it starts loosing conductivity
For trying to fix that - I'd first try powering the Wifi module from another source. If the issue disappears - yeah, that's power interference. If not - that's either vibrations on wifi module, or issue with the camera and not with wifi module.