This is a common fear that I try to help women to let go of because, in most circumstances, even if a nosy neighbor or scared family member called 911, it is easily remedied. (Another midwife and I did a series of in-services for EMS personnel around our county and were able to explore this issue from many different sides - it helped not only when we *did* transport, but also when we called and a transport never materialized.)
'Round these parts, fire dept. EMS appears first. Second comes any ambulance called and third is law enforcement, but only if there seems to be danger or some sort of physical threat to the other EMS personnel.
While it seems that a note on the front might help or sending someone to the door to say "all is well," their rules and protocols require them to see and speak with the laboring mother herself - even if she didn't call. They will offer/insist on doing vitals; they are easily refused. ("No.") They will ask if you/she wants to go to the hospital; also easily refused. ("No.") They will ask the laboring or postpartum mom to sign AMA; refuse-able, but also not the worst idea to sign it unless of a religious, spiritual, ethical, or flash-of-a-reason not to. They do not *have* to have anyone's signature to leave your home. Calm requests will be met MUCH less angrily (and with MUCH less risk of bringing in law enforcement) than hysterical or screaming pleas for privacy. ("Thanks for coming out, but we are doing great. We won't be needing your services anymore." <shuffle, shuffle on their part "Do you want to go, ma'am?" "No!"> and that would typically be the end of it.)
We learned that EMS is always braced for violence - domestic or drug - and especially if there is blood present, they are *really* going to want to/need to assess (hence having to see mom for themselves). They travel in packs for safety reasons (including that of the "victim") and it is why they could never just leave when grandpa meets them at the door and says through chain-locked door, "oh, sorry... everything's okay now." Looking at it from their viewpoint, it is understandable why they would need to talk to the mom themselves.
Avoiding this whole scenario is the best idea of all, however. Even with neighbors you don't get along with, perhaps sending over a baked pie with a gentle note about laboring at home (you might even consider *not* telling them about the birth-at-home part) - or having all family members who *might* be present really, really understand that noise, blood, vomiting, etc. are perfectly normal and if they aren't prepared to be 100% happy with it all, they perhaps should not be invited (don't need to tell them that - but, oops! labor happened so fast, we just didn't have time to call everyone!).
I think the best advice we learned from the EMS people was that the calmest person in the room was the one most trusted. It might not seem fair or right, but was the overwhelming attitude with over 500 EMS we taught about homebirth and homebirth transports. So, even if you are wiggy mad your neighbor called or your meddlesome sister-in-law freaked out, find that place of peace just long enough to tend to getting your birth space back to yourselves and deal with all that later.
I hope this helps a little.
Barb Herrera