I skimmed the entire paper, so a few thoughts.
This study takes place in the Netherlands, so there a few differences. Notably, almost 75% of patients were referred by their GP and many of them were already on antibiotics. Also, EMS in the Netherlands is run by RNs who have taken extra training, so that has some potential confounding there when looking at a US system.
Still, before training, only 14% of septic patients were correctly documented as such by EMS nurses, after training it increased to 41%. The TTA for the usual care group also dropped about 20 minutes after training.
There were also mostly short transport times.
The study population was healthier than many other sepsis studies, which focused mainly on septic patients already admitted to an ICU. Therefore, only a small amount of these patients had actual septic shock (around 3%). This probably also explains some of the long time to antibiotics for the usual care group (no EMS antibiotics) and also the low mortality rate.
The time to antibiotics for the usual care group began at triage, not at physician assessment.
The TTA in the usual care group, despite ranging from 36 minutes to greater than 240 minutes, did not impact survival either.
Older studies that looked at TTA dealt with much longer times than the usual care group. Those studies had TTAs ranging from 2-5 hours, as opposed to the one hour ish in this study.
I couldn't really find anything on patients who were "inappropriately" given antibiotics by EMS, which would seem like a very obvious thing to consider when using SIRS criteria, which isn't the most accurate test in the world.
So basically, who knows. Perhaps even earlier antibiotics are superior for a small group of very severe sepsis cases, or perhaps the system in the Netherlands is efficient enough that the improvements in EMS aren't helpful.
Most likely, as Remi said, antibiotics are better when given quickly but only up to a certain point, which was already reached by the EDs in this study.
Personally, I've yet to be convinced that EMS antibiotics would be useful except in the most rural of places.