Yes, but it doesn't require the trial to be stopped for efficacy. The FDA recognizes there are many reasons the DSMB may think it best to continue.
It would be very difficult and rare for the company to over-rule a DSMB rec. The DSMB is entrusted with the responsibility to make the appropriate recommendation.
In Flemings DSMB book he says:
"In order to facilitate continuation of the trial in the unlikely event that the SC rejects the DMC recommendation for termination, the SC must maintain confidentiality of all information it receives other than that contained in the open reports until after the trial is completed or until it has made a decision for early termination. If the SC does decide to continue the trial, in addition to maintaining confidentiality of such information, it should also be blinded to subsequent closed report information. Because of the problems regarding confidentiality should the trial continue, the practice in some trials is to initially unblind only the SC chair and a sponsor representative when a DMC recommends early termination. This practice protects confidentiality, but at the cost of a narrower perspective with regard to whether or not to accept the DMC recommendation."
I don't think it is black and white. And the prevailing wisdom is to trust the DSMB to make the right decision after considering all aspects of the data.
“No single statistical decision, rule, or procedure can take the place of the well reasoned consideration of all aspects of the data by a group of concerned, competent, and experienced persons with a wide range of scientific backgrounds and points of view.”
I believe that is common text in many DSMB Charters.