A surge protector is just that, it protects against spikes (surges) of voltage from the power company, that's it.
I've read the junk on the box too, My homeowners Insurance will do more for me than trying to wring out money from a company cranking out these protectors.
Who would you file a claim with? Once filed, you would be on the merry-go-round of comapnies claiming it's not their responsibility to pay. "it's the manufacturer", "It's the distributor", "It's one these insurance companies", etc, etc. In the meantime, Your insurance company could have a check off to you and you'd be whole again.
I had a "near" hit lightning strike last year about 50 ft from my house. D* covered the damage to the LNB's and one STB through the protection plan. My insurance company covered the damage to my receiver, XBOX, TV, CD jukebox and several kitchen appliances.
Oh, BTW, the "surge" protectors that my gear ran through were fried, along with my old fuse box, several outlets and some wiring. Luckily I was home and thankfully didn't have any fire related to the strike. The tree that was hit wasn't so lucky. It's a good thing the water was still running (if you know what I mean
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I now have whole house protection, but lightning is and will continue to be something that cannot be controlled or avoided.