The incident in that episode of television was mostly pure fantasy.
There are 35 blood type groups recognized by the International Society of Blood Transfusion, but for simplicity's sake, most people only really need to know about the two most important ones: ABO and the Rhesus D.
Although there are hundreds (?) of other antigens, O- blood is the universal donor, and there's no reason that someone cannot "ever" receive O- blood, unless they are Jehovah's Witnesses. As all blood types will also contain other antigens, and there are none specific to O that would make it truly problematic*, not getting it in an emergency could result in death. A transfusion reaction not involving the A, B, or most common Rh types can occur with any blood type at all, none specific to O-. If the patient can never receive O- blood, they could never receive any other blood, either.
There are blood types that are very rare and very valuable for that reason; one is called -D-.
The Rh blood group system is the most polymorphic of the human blood groups, consisting of at least 45 independent antigens and, next to ABO, is the most clinically significant in transfusion medicine.
The most common Rh antigens are D, C,c, and E,e. Rh- means there is no D antigen on blood cells. One (or both) of the other two are present, and they are not specific to ABO type cells. One blood group, called -D- (or D--) has no D,C/c, or E/e antigens. There are only 110 such donors in the world on the International Blood Group Reference Laboratory database, of which 80% are in Japan.
Yet it's not the rarest blood type. Rhnull is the rarest, as it expresses none of the 60+ Rh antigens due to a mutation in the ability to express Rh at all. There are only a handful (is 8 a handful? Is 9 pushing it?) of registered Rhnull donors, and only ~40 individuals identified worldwide. They have been called the Golden Donors, and theirs the Golden Blood.
So, I cannot imagine a scenario where a person cannot receive "only" O- blood under any circumstance.
In real life, in a life threatening emergency, O- blood ("washed" if it is available), is given. If the patient is visibly hemorrhaging out in front of the medical team, they don't care if the first unit or two is washed or not, O- is given while the patient's blood is being typed and screened. In non-emergent cases, blood is typed and crossmatched, which takes longer.
So, it's possible that some individuals need a rare blood type, but it's not based on the combination of "O-".
*There is only one that I could find in the literature, which involves a donor who has been exposed to Norovirus and a recipient who has also been so exposed. I don't know the severity of the reaction. But it has nothing to do with the Rh factor.)