My take on this: It's a slang usage. Even as a native, I was just guessing at the meaning, until I found this on the internet:
""
Wrench: 1. A tool that is used to tighten a variety of bolts and/or nuts
2. The awesome guy or gal who works at your local bike shop and fixes your bike with tender love and care (even when it is in sad condition).
""
By extrapolation: I think it's a slang word for anyone that works with a wrench, or ostensibly, anybody who works in maintenance and repair, particularly of large, mechanical and tool-requisite structures..
Apparently BP themselves have a common pseudo-slang: "turn a wrench on (a thing [usually an oil rig] ) ", meaning to "work on" which is in BP slang a direct reference to work done on an oil rig. Apparently there are factions within the group who view working on a rig, as a prerequisite to understanding the oil business.
Hope this was close to what you were looking for.. luck/life