Spoon brakes and other devices pressing down onto the tire were not allowed at the 1901 trials, as they are ineffective when the tire loses air (from R. Henry's article, quoted in my previous post).
As Steve Maasland suggested, early brakes indeed mostly attached to the fork blades and seat stays (according to R. Henry, article in a recent issue of the magazine of the Confrérie des 650). In fact, according to Raymond Henry's article, the various tire sizes, often rather close in rim diameter were designed to accomodate different tire widths in the same basic frame.
Basically, the outer diameter remained constant, and to get a wider tire, you used a smaller diameter rim. The brakes, attached to the stays, could slide up or down to accommodate the different rim diameter (like cantilevers do, if the braze-ons are moved).
[I can see this being useful, as BB height and trail won't be affected by tire size. You just get different wheels, and tune your bike to the conditions.]
But according to R. Henry, the reason for this was more mundane: the same jig could be used by the builders for all kinds of bikes, with all kinds of tires.
The article goes on to explain the various sizes 700 A, B, C, 650, etc. and how they interrelate.
Of course, this was written from a French perspective. Practice in the U.S. and Britain may have been different.
Labor-saving standardization isn't new to the bike industry. Back then, most companies offered many models in one, two or three sizes only. It was with this background that the famous technical trials were started to change everything.
Jan Heine, Seattle