No, I don't think people are particularly more busybodyish here than elsewhere. It is just that certain aspects of life which seem completely normal and reasonable in some other countries are regarded as odd, irresponsible or inconsiderate here. While I'm sure that that's true of just about any two cultures, there is an emphasis here in being rule-abiding and the "correct" behaviour is seen to be that which does not disturb anyone else, does not cause tension in the collective. There is not much emphasis on one's personal rights or entitlement to do or to get something.
With regard to dogs, this is particularly apparent.
The overwhelming majority of people in Switzerland do not own dogs. They may wish to, or not, but the fact is that many more people rent than own, and since many tenants and owners live in flats/apartments not houses, and since the tenancy contracts (or the rules of a governing body of co-owners) of flats/apartments very often prohibit keeping dogs (and often also cats)... people have far less contact with dogs than in some other countries where keeping a dog is perceived as sensible (for security) or obvious (as part of the family). Therefore, in having a dog - at all - in urban Switzerland, one is already doing something at least a little unusual.
Now add to this the fact of all those people having grown up in accommodation where dogs were not permitted... and you have a population of people who do not automatically know how to deal with dogs, and who, furthermore, find themselves more readily disturbed by things that dogs do (bark, whine, smell, shed hair, jump up enthusiastically), than had they always grown up with dogs around them.
If a dog-owner arrives from a culture in which keeping a dog is seen to be natural and obvious, and on top of this in which the enforcement of one's individual rights is strongly practiced, there are likely to be conflicts. If, however, the dogs are trained, well-behaved and stay at the owner's side, and if the owner is friendly, polite and not asserting an entitlement, the initial wariness quickly dissipates, and things are fine.