Safety of old, unopened bottles of ketchup
Assuming that there are no apparent problems with it (either from storage method or upon opening and inspection), I am one to agree with StillTasty in this case and say that you would not likely encounter any problems making barbecue sauce. They say twelve months, though.

For the sauce though, not only will the long, slow boiling help; but the ketchup is likely chock full of high-fructose corn syrup (which acts as a preservative), and you will be suspending more sugar (again, a preservative) in it.