It seems a bit unlikely that the NBA had such leverage that they could *force* that pointedly undemocratic, US-dominated organisation, the World Bank out of Narmada, but could not persuade the people of Gujarat or Madhya Pradesh to support them.
More likely is that the World Bank was willing to promote development in India when they were in competition with the USSR for influence, but less willing when India's growth meant that they were effectively promoting a US-competitor. The NGOs just manufactured a post-festum justification for the shift in World Bank policy.