There is NO distinction between "emergency personnel" and "the cable guy" being in the same room as you when you make a VRS call. It simply doesn't matter. The FCC does not make that distinction. "Oh, wait, it's a cop in the same room, it must be okay to interpret this call because it's gotta be an emergency."
The FCC has been quite clear that Video Remote Interpreting (VRI) is not allowed. They've issued at least two decrees reminding VRS providers that this is not permitted. I'll link the decrees in a bit, but suffice it to say the FCC has 'em on their website. Again, the FCC does NOT say, "but, but, but, 911 VRS calls to police, fire, or ambulatory personnel in person are okay."
I'm doing advocacy for VRS in the midwest now. It's my responsibility to know enough about the rules and issues of VRS to answer questions and gain support for VRS with issues like 911 and true number calling. I thought the same like you once -- come on, it's free interpreting, I should be able to use it anywhere with anyone I want. Nope. Not allowed.