Interesting. When I saw this, I wondered if it was to match another standard gauge that was judged to be superior. But, looking at the list of rail gauges on wikipedia[0], 5'6" is the gauge for railways in India ("Indian broad gauge" to be specific). The initial BART rolling stock seems to have been build by Rohr, Inc.[1], which is based in California. So it seems unlikely that they were benefiting from any economies of scale from Indian rail construction. Rohr also seems to have built rolling stock for the Washington, D.C. metro, which uses a near-standard 4'8.25" gauge[2].
Perplexing.
[0] https://en.wikipedia.org/wiki/Track_gauge
[1] https://en.wikipedia.org/wiki/Rohr,_Inc. (you'll need manually add the period to the end of the URL, because of how HN converts this into a link)