A couple thoughts about the examples you provided:
1. You said: "There's an exception like 'I have no husband.' because I can't have more than one husband." <-- True, but more generally, I would say this applies to any situation where people typically only have one of that thing. Most people only have one husband, of course. But "car" would be another good example, or "house." Most people talk about their car or their house in the singular. Most of the time you wouldn't say "I don't have any cars" or "I don't have any houses." -- you would simply say "I don't have a car." "I don't have a house." Hence, "I have no car." "I have no house."
2. In many of the situations that appear to contradict the countable/uncountable rule, "no" is being used to emphasis "not any" or "not one." This is true for the politician example. "No politician tells the truth." is expressing, "There is NOT ANY politician out there who tells the truth." "NOT ONE politician in the government tells the truth". Of all the politicians out there, not a single one tells the truth. That's why it takes a singular form here. So it might be helpful, in cases where it appears to contradict the countable/uncountable rule, to try substituting "not any" or "not one" for the word "no" in your mind, and see if this solves the problem.
Just my two cents. Not sure if this helps.