There’s a new twist in the buyout boom roiling corporate America: a growing skepticism among shareholders and the boards that represent them over the value of such deals.

Whether it’s the directors at Cablevision rejecting a sweetened going-private offer or Health Management Associates’ decision to do its own recapitalization rather than be bought by others, there’s a building backlash to the record-setting pace of private-equity and management-led takeovers.