I think that they knew there is reasonable chance the director might support them and trusts them. They worked on this system for months, it is unlikely that "legendary leader" found about whole thing when they walked into mission control. They did not knew whether whole thing will succeed overall, but at minimum they did had pre-existing trust.

People are not dumb. They know politics of situation they work in. These people were not random renegades ignoring any authority on principle or some such.