Hi
Back of the 4.5-18 book says:
"The warranty is available to any owner of an AR Optics Riflescope."
Maybe the rimfire one is different?
That's interesting, this is what Bushnell has on it's webpage for the AR optics warranty
bushnell.com/global/customer-service/warranty-information
Lifetime Limited Warranty
Since 1984, the majority of our Bushnell sports optics products have been covered by a Limited Lifetime Warranty. Bushnell Outdoor Products guarantees these products to be free of defects in materials and workmanship for the lifetime of the original owner. These warranties do not cover consumer caused damages such as misuse, abuse or repairs attempted by someone other than our authorized technicians.
Binoculars (H20, Legacy, Marine, NatureView, Off Trail, Powerview, PermaFocus, Spectator and Trophy XLT)
Riflescopes (AK Optic, AR Optics, Banner, Rimfire Optics and Trophy XLT)
Spotting Scopes (NatureView, Sentry, SpaceMaster and Trophy XLT)
Telescopes (excludes North Star Telescopes)