I think your comment cuts to the very heart of why we have the hearsay rule. Notably, today's decision is really just a follow up, in my mind, on the Court's decision a couple of terms ago that really cut the heart out of a lot of hearsay exceptions, at least in criminal trials. I'm not recalling the name of the decision right off hand, (starts with a C?) but it was a 2004 opinion also written by Justice Scalia. In that opinion, Scalia held that "testimonial" hearsay could only be admitted under a "firmly-rooted" hearsay exception, which would presumably be one that existed at common law at the time of the adoption of the Constitution. Like today's decision, that opinion was based on the confrontation clause.
By the way, thinking more about yesterday's question, I think part of the question depends on whether the 911 call is considered "testimonial" evidence. Otherwise, I think it might get in regardless of whether it is hearsay or not. Seems like it could be either an excited utterance or a present sense impression.