Getting a FAC is not as easy as just having an interview and waiting a few months.......... For starters you have to prove you have the land and need ie:pest control] and/or an official rifle qualified range to shoot at. The FO in charge of you application would need to visually inspect your land [same as when they confirm your storage is up to code]. This is actually in most cases the hardest part to qualify on. There are not that many official rifle ranges in the country, so unless you are lucky to live near one or have a requirement and space for one on your own land, you most likely you wont get one. Some people require one, such as gamekeepers, which would then mean inspecting your employers land etc. Then of course you need the interview, which is not only a psych eval, but a character eval. Then the usual referees, get your GP to sign off and to officially state you are in good health physically and mentally and so on.
Getting a Shotgun certificate on the other hand is easier to get, but usually 1 because shotguns are not as "lethal" [legally] as rifles. EG: you cant use/qualify for a rifle on your own land if there is no where on your land that is more than 1500 feet away from a road, and its illegal to fire a rifle in the open towards a road that is less than 1.5km away. With a shotgun these ranges are much more reduced [for obvious reasons] and there are many more clay pigeon ranges than rifle ranges. On top of that the ammunition you can get for shotguns is significantly less lethal than even standard rifle ammunition for a .22 long, shotguns pellets are non lethal when ricocheting, coming back down to earth, and cant even penetrate a decent coat over 30 metres. So long story short, unless you own a substantial amount of land or become a member to one of the few rifle ranges, its very unlikely you would even get past that initial stage. As a side note, i was able to get a shotgun cert at the age of 14 with the sponsorship of my dad who was also shotgun certed. That's not allowed with FAC's under any circumstances.
If one can pass the steps to get a FAC there is no logical reason they shouldn't be allowed a BB gun, other than due to specific wording on a law which from the sounds of it is kinda flawed/didnt put into consideration people who have a FAC and wanted to go airsofting!