This argument is a little over-long, so to summarize: By allowing others to use the "core" of BRP free of charge, Chaosium could create a secondary market for BRP-compatible material, and boost the sales of their own BRP line.
My premise is that Chaosium wants Basic Roleplaying to do well, perhaps even taking a little business away from D&D and White Wolf's Storyteller games. Chaosium's tendency to do small print runs, to the point where their books become instant collectors' items, belies this premise, but I'll run with it anyway.
As far as the current market is concerned, BRP is a johnny-come-lately to the "generic system" market. Never mind it's been around forever; a lot of current gamers haven't heard of it, and others would be reluctant to jump systems unless it supports their particular genre or play style. Chaosium, as a four-man operation, can't hope to compete with the likes of GURPS, much less the D&D juggernaut.
Therefore, a clear, legally binding statement from Chaosium allowing others to reference "core" rules free of charge would enable a secondary market of "BRP-compatible" rules extensions, settings, and adventures. Said market would consist mainly of small PDFs on DriveThruRPG or YourGamesNow; in today's market only an idiot would do a print-run of a full $30 book without establishing a market for it.
By "core" rules, I mean the equivalent of the old BRP pamphlet: primary and secondary attributes, the percentile skill system, a common subset of skills, the essence of the combat system, and the principle of increasing skills through use. Since Chaosium used to provide those as a free pamphlet, now allowed to exist on a web page, and now presents a version in their free Call of Cthulhu quick-start, I can't see how endorsing an updated version would lose Chaosium sales. WotC didn't suffer during the d20 boom, since they still had the brand, and could make the final call whether a product had the "d20" logo on it.
Unlike the d20 gold-rush, the BRP is small enough that, while 90% of it might be crap, it will be easier to find the 10% that isn't crap. And, of course, if you want guaranteed good stuff, you could buy from Chaosium. Discovering a wealth of add-ons and customizations for a new game would, as the marketroids would say, "delight the customer".
Even better, Chaosium might allow anyone to drop "Core BRP" wholesale into a game, to make it "BRP compatible". (Which might not be the same as "Official BRP".) If you're trying a new game, ideally you'd buy a single book complete with setting and rules. A huge problem with, say, GURPS, is that you have to pay $75 for the 4th Edition Basic Set before you can use any of the $35+ other books.
OGL itself might not be the solution. The specific provisions I'm thinking of designate "open content" from "product identity", and not charging for the former, but perhaps they're not precise enough, or have other legal entanglements. To strengthen the BRP brand, though, maybe Chaosium would require "Core BRP" to appear in its entirety, unedited, separate from any non-core content.
Another possibility, since Mongoose already took the OGL hit, is to design a "BRP-compatible" system off MRQ, designate it as OGL, and release it free a la GORE. It would be the equivalent of the old BRP pamphlet, maybe with a few extra skills, and if Chaosium objects to even mentioning BRP, then said ruleset would have some alternate, but suggestive, name.