For example, a local store I love to frequent is going out of business. I and the employees go to court for an order to stop it, based on them losing their jobs and me losing a great place to shop. Maybe we will suffer greater harm than the chain will if it can't close this one store right away. But unless we can convince the judge we have a legal basis for our lawsuit and we are likely to win in the end, he isn't going to order the store to stay open. Balancing harms makes no sense unless the plaintiff has a legal right to assert.
It is a continuum thingie, but since the Terri case is factually driven it cannot be characterized as Terri's parents having a frivolous claim. Above are the ins and outs on the matter, which in the end kind of suggest that the court can do whatever the hell it wants within wide limits. But with an impending corpse, in the case, it really can't.