Nope, they they were built like it. I have seen others identical to my rifle and the rifle that you have seen.
The Birmingham Gun Trade was famous (notorious?) for using up old parts.
I'm sorry to have to say this but I think that what you saw was simply a miss-dated (by the dealer), between the wars BSA commercial that someone had put target sights on. Before all these new-fangled Swings and Metal Mickies, SMLEs were commonly used for target shooting.
I think your right. I've seen it twice and it feels as if it's just come out of the shop!. Mind you I'm a complete beginner at this Enfield business so no idea really. Still, I would prefer it to modern and it might be cheaper and much more interesting.