They didn't make promises, you're deliberately using language incorrectly to make your argument sound better. They could not make promises, they're not in Government!
Oh really.
Official leave campaign video:
Watch at 3:14
"Every week the UK pays £350 million to be part of the EU. That's £350 million that could build one new hospital every week. £350 million that could be spent supporting our doctors and nurses."
No a complete promise to spend £350 per week on the NHS but damn, it's a pretty strong hint that if you vote "leave" that is what you will get.