The manufacturer is recommending that particular type of lube oil be used because of the high pressures associated with pcp airguns, and the small likelyhood than an individual may get volatile petroleum based oil into the high pressure system or barrel where it can detonate and cause injury.
Here's what we use and where:
Pure silicone diver's lube, for non moving, static o-rings. Don't put silicone grease on any threaded parts.
Krytox GPL-205 for moving o-rings
Ballistol or Frog Lube cleaners on the outsides of the gun to prevent rust and acidic handling damage.
Pure silicone oil (commonly known as RC shock oil) for lubing pellets (if going that route)
This list is by no means exhaustive or exclusive.