Why should I repair/replace roof just because it's old?
"Shingles torn" "Nails showing"

You very probably have leaks you have not yet noticed. If you re-roof now, you might not rot out the roof deck and need to replace it as well. If you wait until you have leaks you notice, you may find that you're rotted out the roof deck and be looking at a far larger bill.

However - don't hire ANY contractor that drives by, looks at your roof, and rings your doorbell offering to replace it for you. That sort of "drive-by marketing" is typically associated with the absolute lowest form of "wannbe contractors", often mobile units that won't be around when the new (shoddily installed from the worst materials) roof leaks. Look up established local firms and invite them to make a bid.

Your insurance adjuster is wise to the tactic you plan to engage in - if the roof was not maintained in good condition, they will probably deny the whole claim (you neglected the house) rather than buy you a new roof. They know what old shingles look like, even after they have been torn up by bad weather. They probably even have "before" pictures of it, with dates, in their files.