Some of the language used (walk on vs. scholarship) isn't exactly the way we think about it. We all get that scholarships are technically renewed each season. However, we also get that coaches typically don't even consider not renewing those scholarships (unless it's an academic or behavior issue). So the language that is often used is that a "scholarship player" is a person who will be on scholarship until graduation. A "walk on" is someone who is not. However, that doesn't necessarily mean that a walk on player isn't on scholarship for a given season (they never just sit empty).
So hypothetically, if Joey King was willing to consider the scholarship next season and we'll see (probably walk on) after that. . .I could see him being considered a walk on. They do this because they don't want someone later saying. . ."hey, you pulled Joey King's scholarship", when in actuality that had always been the deal. So they just call them walk ons.
My point in this long ramble of semantics, I wouldn't assume that just because King could be coming as a "walk on" that means we still have two locks in recruiting.
My guess is it's a situation where Pitino has been real upfront. He's probably said, "we have a chance for a couple other guys this year, and if we don't get them a scholarship could be available for you for the 13-14 season. After that, we'll see."