I think you may be dramatically overestimating how much the Canadian military cares about the FBI. We've been FIGs since at least the 80s, long before the FBI had Field Intelligence Groups.
It's a fairly straightforward acronym - intelligence operator = Int Guy, throw in Fucking and you have FIG. Figs are fruit, infanteers tend to consider anyone not in the infantry to be lesser soldiers, it just makes sense.
I know we've been abbreviating intelligence as Int since at least the 40s (Canadian Intelligence Corps was abbreviated C Int C from 1942-1968, the modern Intelligence Branch has worn INT shoulder titles / rank slip ons since it was founded in 82.), I suspect even longer before there was a separate Intelligence trade
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