Connotation meant by “B of A” and “A's B”. What would be the differences?

Question

Do you agree with the interpretation of the following three example sentences?

1. I don't want to be involved in the problems of my boss.
   The boss probably deals with some problems. e.g. slow sales, product quality issue, customer complaint

2. I don't want to be involved in my boss's problem.
   This implies a similar case as above one, but with only one problem.

3. I don't want to be involved in the problem of my boss.
   Probably the boss himself has caused trouble. e.g. a misconduct

If you agree, then

Q1) Why is "my boss's problem" likely to mean that my boss has ONLY ONE problem?

Q2) why is "the problem of my boss" LESS LIKELY to mean that my boss has only one problem, but MORE LIKELY to mean that the boss himself probably has caused trouble?

Answer 1

Sounding like a native English speaker (any standard variety of English)

I disagree with the interpretation provided for this simple reason:

My boss's problem [singular] and My boss's problems [plural] are the simplest and most idiomatic way of expressing what ails the boss: one problem or more problems than one.

The "of the" point is just awkward. In actual speech, using the "of the" option here sounds non-native or non-idiomatic.

• I don't want to be involved with my boss's problem OR boss's problems.