Interesting. Do you know of any printed rule set prior to the BBCCo putting it forward as their creation?
Edit: The rules of BBC Co pool, which is basically the same as eight ball but with reds and yellows, was in the 1908 BBC Co rulebook (page 117) but was not in the 1905 rulebook which did not go to page 117.
Unfortunately not handy. The historical record when it comes to the rules development of the main forms of pool is sparse at best, as at the time in the early 20th century when they took recognizable forms, pocket billiards was a disreputable game played in dark, smoky pool (that is, gambling) halls, in contrast to the upright, gentlemanly game of carom billiards. Harold Wilson wasn't making things up about the public perception when he wrote
The Music Man.
But it's logical. Firstly, the idea that eight-ball pool was created out of nothing doesn't pass the sniff test. It's a natural development from basic pyramid pool, which dates to the late 1700s. In pyramid, whoever sinks the majority of the balls first wins; for 15-ball pyramid, that would be 8 balls. To simply designate one of those balls, the middle of them, as the last that must go in is a straightforward way to make the game more complex, increasing the strategy. Likewise, splitting the balls so that one player can only pocket the balls lower than 8, while the other pockets the ones higher than 8 is also a straightforward addition of complexity. Those are the two essential things that distinguish eight-ball from basic pyramid pool, and both date from no later than 1900. The claim that eight-ball isn't derived from basic pyramid is unsubstantiated, and illogical.
Of course, all of that requires the balls to be numbered, but they already had been since the mid 1800s, as required by the game of 61-point pool, where each ball is worth its number in points, making a total of 120 available points, and the player to get a majority of points (as opposed to balls) wins. That variant was popular in the mid 1800s, but by the 1880s it became apparent that one could simply win by targeting the highest value balls and winning with fewer balls than the opponent, which was seen as unsatisfactory. So two different ways to deal with the problem were introduced.
One was to do away with the varying point values (in that sense going back to basic pool), but requiring that winner to accumulate a large number of points over continuous play with the balls re-racked when the table was cleared. The tweak in 1910 of re-racking with one object ball remaining, which was done to discourage defensive play, is what created modern straight pool.
The other was to require the players to aim at the balls in numerical order, creating the category of rotation games. It was for ease of play of rotation games that the practice of using a distinct color for each ball arose, but the limit on how many distinct colors are practical led to repeating the colors with solids and stripes. And while 61-point rotation is still sort of a thing, it can get repetitive when the 11 always wins, as would be the case if a player runs the rack. So the added gambling element of each player having a different, random "money ball" gave us Kelly pool, which is why multi-colored pool balls are still sometimes called Kelly pool balls. However, the disrepute of the gambling around the game (once again nodding to Mr Wilson) lead it to be banned in many places, and the simplification of using the same money ball for all players got around that. By around 1920, the 9 became the standard money ball, though it didn't become that prominent until TV wanted a fast paced game.
But to return to the BBC Co., doesn't it seem more logical that they would introduce a product to capitalize on a recent trend while claiming it makes the game easier to play and more visible for spectators? After all, if the game is played without called shots (which date from the 1880s, but aren't often used in casual games), then the balls don't need individual numbers. That's all they were doing, not creating the game themselves.
And as a sideline to that, the idea that English-style eight-ball/blackball retained some older form doesn't jibe with either the dubiousness of the claim that it's the original form or the fact that pub pool tables were almost non-existent in Britain until the 1960s, long after the solids-and-stripes were standard. They didn't retain a continuous use, they revived an old equipment variation because it is cheaper to replace a missing ball if they all look the same. But, as I said, that's a sideline, as there's numerous other elements that show that British blackball is a relatively late creation, not a continuation of an older form.