Here's a closeup. It looks like it wants to create a new plant at every node.

It's not Acaena......look at Leptinella squalida.

Here's some info from a ground cover vendor:
http://www.stepables.com/5/Leptinella_squalida_New_Zealand_Brass_Buttons.html

I recognize it as being that one also. Might this have come from a source other than the arboretum, such as a donating member or a participating vendor - that was mistaken about the identification? The Seattle arboretum has a fairly big area near the offices where donated plants are sold each year; nearly all of the other plants displayed at the main spring sale (and other sales held at the arboretum) come from commercial sources, without the arboretum staff being routinely involved with what each item is being sold as.

Thanks everyone for the information. I realized it looked "similar" to the Leptinella, but just assumed the arboretum got it right.. I grew the 'Platt's Black' cultivar about a year ago. It didn't live very long, so I didn't have the plant to compare it to.

Of, course even the best Arboretums make mistakes. I believe plant propagation for sales is done almost entirely by volunteers. Most of what they sell is propagated from the Arboretum's own plants, but I have bought plants that appear to have been donated by wholesale nurseries. Some of the plants do come from volunteers and others. And of course tags get lost.

It was a $3 plant, so it will be an inexpensive way for me to try again with this species.

Here is a link that might be useful: Cotula (Leptinella) 'Platt's Black' at Annie's Annuals