This is a grossly oversimplified version of the story. The Golden Gate bridge authority asserted that the additional weight of BART on a lower deck would reduce

This is a grossly oversimplified version of the story. The Golden Gate bridge authority asserted that the additional weight of BART on a lower deck would reduce the clearance underneath the bridge sufficiently that naval vessels wouldn't be able to pass. The study supporting this was paid for by the bridge authority, who had a financial incentive to prevent BART from going ahead - nevertheless, there was a risk that Marin might never have got BART even if the population had voted for it, and would still have been on the hook for payments. This depressed support in Marin sufficiently that it might have dragged the regional vote below the 60% threshold required for the entire system to be built, and the other counties pressured Marin to drop out against their will. If San Mateo hadn't chosen to drop out earlier, there's a decent chance that Marin would have service today.