Justine888, the same things could happen to a much older child or even to an adult. What about when she is 15? Even grown-ups can panic in a fire or open the door to a murdering maniac. It has been known. Are you saying she is never to be left alone, because regardless of the dangers, you don't trust the people around?
But that will always be the case. Sooner or later we all have to screw ourselves up to let our children tackle a dangerous world. The question is just when do you start, how do you start, how quickly do you work up to it.
It seems to me that part of the problem for the OP was that she and her dp had not discussed this beforehand; he sprang it on her a bit suddenly.
To my mind, leaving a 6-7-yo alone for a few minutes in daytime is not ott, asuming:
that you have discussed it with her beforehand
that she is happy with the arrangement
that she has agreed to stick to certain rules (e.g. don't answer the door, don't come and look for me, only leave the house in case of fire etc)
that you feel that this particular child is mature enough
I did this with both of mine at that same age, but would not have started any younger- I wouldn't have felt safe trusting a 4 yo.
By the time dd was 9 or 10, I was trusting my her to walk down to the local shops, to walk to school on her own (when her disability allows), and to stay at home for slightly longer periods (say an hour). I also trusted her to play unsupervised on the beach on the very quiet small island where we spend our summer holidays.
Now that she is 11 I allow her to take little brother (7) to the shops or to the local library, and to stay at home in the daytime for several hours. I also trust her to go swimming with friends (same quiet island), as long as she promises to stay in the shallows and never to swim alone.
Next year, she will be going to secondary school, which may involve going to school by public transport. At this stage, I think it is reasonable to allow her to go into the town centre in daytime with a friend of the same age.
Basically, my idea is to build up slowly and gradually, letting my dc's see that every new privilege rests on the idea of responsible behaviour. Sometimes I feel scared about the other people out there (and the cars! and the buses!)- but then I realise I'll feel the same when they are 15, and when they are 18, and (heaven help me!) when they are 45!. I have got to let go at some stage, and my experience as a university teacher suggests that it is not wise to leave it too long.