IBM 5160 math copro switch

Sifting through my XTs and clones... I've had three so far with no math copro (8087) fitted, but switch 2 of SW1 is set to off. IBM docs say off is "math copro installed" and on is the "installed" position, i.e. the reverse of what I'm seeing (the minuszerodegrees site repeats this, although I expect that just copied what's in the manual, too). These three machines (two are 5160's, the other a clone) came from completely different sources - it seems unlikely that all three had 8087's fitted which were pulled at some point. Googling a few more system board images, ones with 8087's have that switch on - but for boards without, the setting seems to be pretty much 50/50. Did the meaning of the switch perhaps change at some point (both of my 5160's are late model 256-640 boards), and rather than being a simple installed / not installed it was more along the lines of "software should use it if present / software should never use it"? After all, it's not like the BIOS will do anything with an 8087; it's only there for software specifically coded to make use of it. I suppose it's also possible that users were in the habit of first setting all the switches to off when configuring a machine, then setting the relevant ones to on according to their memory/floppy/video config - and the copro setting just got overlooked. Weird, anyway. Jules