creeduk, I agree with your opinions, here are some comments.....
1) Saving at the same jpg level: If you open an image, do nothing, and then resave it at the same jpg level, yes, loss does occur. JPG is a lossy process, if all the losses when saving were exactly the inverse of the losses when opening then, thoretically, there wouldn't be any loss. But they ain't, so there is! Although the loss very small and basically confined to the difficult parts (for jpg, that means high contrast 45 degree lines);
2) Saving at a higher level: If you open an image, do nothing, and then resave it at a higher jpg level the resultant file will be slightly larger but there will be hardly any useful information there - it will be just a bit more like the previous file was. (observe that the size increases at a slower rate than would for a non-jpeg'ed image.)
3) Do nothing? Dunno why you'd open and resave a file without doing anything. If you did do something, the that something will suffer normal jpeg loss.
Note. Cropping is much more dangerous than just resaving.
JPEG works by chopping the image into 8 x 8 chunks (for luminosity, 16 x 16 for colours). If you crop the top left corner then (unless you chopped off exact multiples of 8 / 16) the boundaries will fall in different places and JPEG losses will accumulate.