Comes down to money. Netflix and Hulu can offer BBC more money. And conglomerates have subsidiaries that deal with each other, their parent companies, their sister companies, etc all the time. Just ask any corporate accountant.

Oh, they're certainly allowed to deal with each other. They just have to deal fairly with each other. The BBC can't continually offer BBC America a better deal than Netflix, or insist on only dealing with BBC America, because that's going to eventually run them afoul of anti-monopoly laws. It's happened in the past: the major Hollywood studios used to own every rung of their business (production, distribution, and exhibition) until Paramount was sued by independent theaters and forced to divest in the late 1940s. Ditto for Bell Telephone, who held a monopoly over production of telephones, construction and placement of wiring, and telephone exchange equipment until the early 1980s, when another US Supreme Court case broke them up into the "baby Bells" (AT&T, Verizon, et al.).

There's still plenty of good reason for limited vertical integration, mind you. For one thing, if you can open a subsidiary that can make profit, the benefits of that are fairly self explanatory. For another, if the market you're entering is small or underserved, it can help you get your product out there. That's how the Hollywood system got its start, more or less, and it's probably a large part of why BBC America was created, because there wasn't all that much of an outlet for BBC-produced content on US television at the time. And, on a similar note, the increased competition can drive up demand in itself. But it's a matter of degree. Get too vertically integrated, or (more to the point) misuse your vertical integration to hurt your competitors (like offering frequent sweetheart deals to another subsidiary of your parent organization) and you're cruising for trouble.

All of which is to say that you're not wrong, really. It is all about money. But it's not just a question of standard corporate greed, even if that's surely a significant part of it.