For people who apply together for a UK visitor visa as parents, or parents and one child, can it be the case that one visa gets approved and the other rejected? Or is it a required that all should be approved or all rejected?
Yes the result can be different for different applicants even if they apply together.
Here is one such example.
In the UK, for example, a big question is always: "Will this person return to their home country once their permission to stay in the UK runs out". If Mr. X applies, they might say "Mr. X is married to Mrs. X, so he will surely return home to her". If Mr. X and Mrs. X both apply, that reason to return home has disappeared. So it's quite possible that each of them individually would get a visa, but not both together.