In this context, 'follow' means that the first statement does not necessarily entail the second statement. That is, 'The FDA may review drugs from a health and safety point of view, but that should not require that the secretary have a blanket veto.'
Here, the word 'blanket' is used to mean 'complete or absolute.' That is, '... the secretary or president should not have the ability to completely reject its decisions.'
Student or Learner