As @Calicaps says, it would be stupid, but not illegal.
I'm not sure about the stupid part. If NHL's LTIR and player insurance have zero connection, then it's two systems with their own rules. So long as Backstrom is on board, LTIR should be a breeze. That part is moot.
While getting off the hook for the cap hit should be easy, gaming an insurance company for ten figures isn't. So the idea that LTIRetiring a player and not filing an insurance claim is stupid doesn't really track. LTIR won't require the intense medical scrutiny you guys were alluding to above, and it's not illegal. Insurance fraud of that magnitude would require that scrutiny, and is absolutely illegal.
Stupid to not file a claim just to see if they'll cover it? Sure. But also stupid to lie to try and defend that claim if it's disputed and you know it's bullshit.
I'm not sure there's ever actually been a dodgy LTIRetirement. Hossa's thing only sounds nutty if you really want it to. The nitty gritty explanation holds water; it's just weird. And if was written somewhere that insurance covered it, then it was probably legit.