Sort of. A powerful fish can actually snap a rod before it breaks the line. That happens quite often with big game fish like tuna and marlin. And I've broken rods just by casting very heavy baits. You'd think the line would pop first, and sometimes it does, but not always. Fishing line usually breaks due to fatigue or damage. But yeah, you could theoretically catch any fish on any set up if you work the fish correctly. The only realistic comparison I can make to what they're saying is if you use a light line on a very heavy rod, you could transfer too much of the load into the line. What makes this fishing comparison moot is that with fishing the forces at play can overpower the equipment, and there's the constantly changing human element of reeling in a fish. Those forces are infinitely more variable than anything you'd get on a guitar. There's nothing happening when simply tuning a guitar that can overpower a healthy guitar string. We're not talking about putting bass strings on a fucking ukulele. It's a string gauge change. Sure, the setup might need some minor tweaking, but going from one gauge to another within a reasonable range for guitar isn't going to fuck the world all up.
I recently accidentally put a G string where a B should go because I grabbed the wrong string and did it quick in the dark. I noticed that something felt off but didn't realize what I had actually done until the next morning. Hey, where's my G string? Why do I still have a B? Fuck! I put the G on the B! No problem. It tuned right up, played it all night, and nothing went haywire. Didn't even sound bad.
... the use of precision tools to measure when setting up a guitar isn't odd or anal...it's about accuracy and consistency, and most every guitar tech probably has several tools in their kit. 
