because of the first sale doctrine
Unfortunately, that explanation doesn't work because Netflix generally acquires DVDs from studios as part of a cooperative agreement
Use your brain. Back before streaming, back before Netflix, back when Blockbuster was king, what motivated the studios to to make cooperative agreements for DVD rentals? If you said "first stale doctrine" you win the prize. The studios figured out they would make more money by taking a cut of the revenues instead of only getting a single sale for a DVD rented many times. The rental places figured that lowering the capital outlay for new releases was a right good plan too. So they came to a gunpoint agreement -- the gun being the first sale doctrine.
The deals with Netflix are little different than the deals with any other DVD renter. On the other hand, Netflix tries to avoid buying DVDs because they're out $20 when it breaks in the mail, versus cooperative agreements which replace them cheaply. But it has a few competitors who buy and rent the DVDs Netflix won't -- and ship them more carefully.
Meanwhile the precedents for streaming absent permission are 100% in the copyright owners' favor. Even if Aereo wins its case, DVD renters are still prohibited from breaking the DVD copy protection. So the owners don't have to permit it if they don't want to. And some have secretaries who print their email.
It's the law stupid. The answer to your question begins and ends with the law.