I believe at the time the terms were used interchangeably, and I think when it was introduced to Brazil the name Judo was fairly new, so he may have felt that Jujitusu was a better, more well known name. Its hard to say really, the history of this stuff gets fuzzy. But Judo is a form of Jujitsu really, so the arguement is really academic.
If I read my BJJ history correctly, I also believe you're right about what was taught to the Gracies, and then they further refined it.
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