I think that would be appropriate if it was a Finnish capture/made Mosin, but it's probably not, seeing as most Mosin's on the market are Russian.
This is strictly speaking true, the Mosin-Nagant used by H?yh? was a Finnish national service variant called the
pystykorva or "upright ears" because of the extended front sights, but in all other respects it's the same rifle as the model-91/30 Mosin-Nagant used by the Red Army (except the barrel would have probably been Swiss or German, and parts of the stock which were Finnish-made.) Judging by the OP's picture, it's even the shorter carbine variant favored by H?yh? because of his slight frame.
During my time in the Sandbox, I heard a few Brits use the term. Could have been they were just messing around, but I'm pretty sure it's a somewhat fairly used Western military term outside the US as well. It might just be however, that US war films like to say it more for dramatic effect, than other countries war movies?
It's my experience that military people spout out some of the worst cliches themselves, though it's mostly self-referential tongue-in-cheek.

I think it's become sort of a life-imitating-art-imitating-life kind of thing.
Perhaps that is something they teach you in the military, to see it not as a tool, so that you grow attached to it and become desensitized to the fact that the only purpose of it is to kill.
Actually, it's more to do with getting Johnny McCivilian to learn to respect his rifle like it was his girlfriend, because if the [censored] hits the fan and your weapon fails because you didn't maintain it properly, people die. You live with it, sleep with it, [censored] with it, and generally are never more than one dive's-length away from taking up arms. Nothing to do with desensitization (we have TV for that) and everything to do with learning the responsibility of being a soldier.