Marin /did/ want it, but after the Golden Gate Bridge authority insisted that the bridge couldn't support the extra deck needed for BART there was a risk that if Marin were part of BART they'd be on the hook for the money without ever receiving service. That, unsurprisingly, reduced enthusiasm - and if a reduction in the Marin vote had dropped the overall bond vote below the required 60 percent, none of the system would have been built, so Marin was kicked out.
That's not what the article says: "On aerial trackways during high wind events – which the engineers knew were not uncommon in places such as Contra Costa County -- the light BART cars could potentially tip over, the engineers hypothesized."
It does say later that it was also a consideration for running BART on the lower deck of the golden gate bridge.