I do know that if you are facing any jail time you have to be provided with counsel. The judge cannot get around that.
You are absolutely correct. To a point.
Once you are in court, and the charge carries jail time, you either get a lawyer or the case falls on appeal on 6th amendment grounds. If you refuse to hire an attorney and you cannot convince the judge to let you represent yourself, an attorney will be appointed in spite of your desire/insistence in self-representation.
But that is not the issue here.
The discussion was about an attorney advising you during police questioning.
While I do not know the specifics of the public defender system in every jurisdiction, I am familiar enough with the administrative cases coming out of DOJ funding issues to feel comfortable stating that income & resources are asked about either right before or right after they get your name straight. If you do not meet the income/expenses threshhold for indigence, you do not qualify for a free lawyer. If you "demand" a free lawyer, you can see a judge and get told you have the $$ and must spend them.
stay safe.
skidmark