J.C. got it right.
To add detail. I talked in November with the head of the trail crew while standing at Tourist Trap (he and I had spent the earlier part of the day walking out to Yaks Wall via Marmot Rocks and then coming back by way of Chalone Peak Trail - he'd never seen these areas).
He and I discussed the climbs to the right of Tourist Trap and the new "trail" that the trail crew "made" while working there. As to the new trail, they didn't make it on purpose, but they had to get rock material from somewhere in order to build up the Tourist Trap staging areas. "Somewhere" happened to be to the right/toward Invisible Cliffs (which is pretty logical).
According to him, the sign is emphatically wrong - there are no "closed areas" there at all. The sign was placed in order to try to keep large numbers of people from "expanding" the cleared areas at the base of Tourist Trap unnecessarily. There are several places in the park that are not "closed" but where this sign is used in this way. The Park Service doesn't have a different sign that they can use - at least not at Pinnacles and not right now.
We did discuss alternative types of signs and alternative wordings that didn't send an incorrect message. He suggested some specific wordings, but I only recall now that I liked one suggestion in particular (I can't recall those words exactly).
This isn't the type of thing though that happens quickly. The trial crew is really, really busy with "triage" of "real" trails (they're underfunded, what a surprise). But I think/hope that in the next several months - perhaps by the next PCAD, some solutions and alternative sign language might be coming along.
Anyway, in summary, I was told right at the site that no, that is not a closed area. This confirmed what I'd been told several times by other park staff about that type of signage in less site-specific discussions.
And BTW, like J.C., I really admire and appreciate your sense of stewardship and concern for climber/Park Service relations. Thanks.