I agree that the babysitter should be in the same house.... but i think the reaction of many posters is alarmist and excessive if the neighbour's house is immediately next door.
If she's next door and the monitor's in range she'll hear the baby and be able to attend to the baby in a very short period.
If there's a fire, presuming there's are smoke alarms, she'd hear them too, and be in quickly.
A break-in, Madeleine McCann style - well, that would surely be picked up on the baby monitor too!.... and if the intruder was so quiet that they weren't, well that could happen to anyone anywhere unless you stand guard over your baby all night!
Boiler breaks down... if you're living in the U.K. at present it's chilly but not dangerously cold. There was no heating upstairs in most houses until the past generation and toddlers didn't die from cold on somewhat chilly evenings!
In summary, whereas I think the babysitter should be in the same house, the risk of her not being is so small that it really doesn't warrant the general, rather hysterical, responses to this thread.