We talked about this in a CPR class once. The biggest reason paramedics don't run is to avoid injury, which would obviously impede their ability to help.
Unless it was really slippery, or if they thought someone was going to flip out to the point where it seriously interfered with the CPR, taking your time doesn't seem like the best thing to do for the victim.
To me this is disgraceful, it sounds like OSHA got involved and made policy something that must surely be counter intuitive. Yes, I know the statistics of small risk- done often, but this is such a sad condition for our special to have reached when people carrying life saving equipment don't move a little faster to save someone.
You wouldn't happen to use a staging server, would you?
Rule #1 in any first-responder situation is to keep the rescuer safe. There are tons and tons of examples where rushing led to mistakes that killed the rescuer AND the patient.
So don't be upset! Moving with caution is not an OSHA rule - it is best practice learned over decades of hard-earned experience.
If you infrequently enter a situation which has a low chance of hurting you, you are probably fine. But if you frequently enter those situations then it's just a matter of time before it happens to you.
Our professional emergency response people should be capable of hustling/running over to the people that need their help while maintaining their composure and ability to think.
It is true that exertion causes a sympathetic response, but hustling/running over to someone doesn't produce such a significant sympathetic response where people can't think straight. I know that it's inherently a stressful situation, but our professionals should be able to handle that, and the additional stress of hustling/running over is negligible.