I don't know anything about the BGJP poles ... but, if I were going with BnM products for Spider Rigging, I'd probably opt for the Capps/Coleman 14' rods. They are a little less stiff than the PST, so they should show lighter bites a little better.
On the other hand, if you watch this video : https://www.youtube.com/watch?v=ePVfPmYLZxI ... as I did (for the first 4mins, anyway) then you will see that, despite the disclaimer, they seem to be very commonly used for that very purpose.
Now, I did notice that the 1/2oz weights being used did put a bit of a bend in the tip. Probably a bit more bend than what a C/C rod would do, and even a PST. I would probably not recommend using more than the 1/2oz weight on a BGJP, just simply for that fact. I have a PST & 2 C/C 14' rods that I use for Pushing jigs/cranks (not a Spider Rigger, myself). I tested them against each other with 1/2oz weights & could barely tell any difference in the amount of bend in the tip between them. Add a little more weight, and the greater limberness of the C/C rods became easily noticeable. I've Pushed jigs/cranks with 1.5oz weights @ 1mph ... and there's a obvious difference in the amount of bend in the C/C rods vs the PST rod. What you don't want is a rod that will bend almost to its max load range due to the amount of weight used + speed at which your technique requires. You would struggle to see when a fish was on the line, plus you'd be taking a chance at breaking or damaging the rod should you hang up the bait.
My opinion on the "not recommended" disclaimer is that it's probably geared towards the use of heavy weights in those methods, and is meant for use as a "vertical jigging" rod ... just to cover the specifics of the warranty.