It's not all that strange. Factotums use spell-like abilities which function differently than spells do, and they have a much more limited number of them but select them from the whole list, so a wizard/factotum is essentially experimenting with what he knows of magic and figuring out how to reproduce spells they don't know using a sort of magical "shorthand" of some sort. I picture it like a wizard sitting there trying out variations on spells he knows ("Let's see, 'solenu samatkahl'...nope, how about 'solenu samatkereh'...'solenu samatkohn'...'solenu samatkiir'--oh, hey, greenish flames, it worked!"), finding something that approximates a spell, and using it with the intent to figure out how you get from Spell A to Spell B later.