I don't think the bar exam is scientifically designed to measure intelligence so that was an odd example. Citing the bar exam is like saying it passes the "Game of thrones trivia" exam so it must be intelligent.

As for IQ tests and the like, to the extent they are "scientific" they are designed based on empirical observations of humans. It is not designed to measure the intelligence of a statistical system containing a compressed version of the internet.

Or does this just prove lawyers are artificially intelligent?

yes, a glib response, but think about it: we define an intelligence test for humans, which by definition is an artificial construct. If we then get a computer to do well on the test we haven't proved it's on par with human intelligence, just that both meet some of the markers that the test makers are using as rough proxies for human intelligence. Maybe this helps signal or judge if AI is a useful tool for specific problems, but it doesn't mean AGI

I love this application of AI the most but as many have stated elsewhere: mathematical precision in law won't work, or rather, won't be tolerated.