You have a lot of your facts correct so I will try to confirm them.
(a) HKS has joint degree programs with a select group of premier business schools including HBS, Stanford, Wharton, MIT and Tuck.
(b) As a joint degree candidate, your applications are reviewed by three committees in most cases: HKS, the business school you are applying to and a committee that overseas the joint admissions.
(c) It is possible that you can be admitted to one program and rejected from another. I generally did not see this happen until recently - and most of the time it is the MBA program rejecting a candidate, not HKS.
(d) If HBS rejects you - you still have chances of being admitted to HKS -- as HKS application specifically asks which MBA programs you are applying to.
(e) You have to check with specific school on their policy of having you apply to HKS once you are admitted. Most schools will allow you to add on a joint degree if you have compelling reasons to do so.
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