I think this post has a big misconception in it. Public defenders are for the destitute. You have to ask for one, and convince a judge that based on your assets and income, you can't afford a private attorney. There's no choice here, if you can afford a private defense, you won't be given a public defender.
I think this depends on the state, I think in a lot of states getting a public defender is just based on the Judge saying that in the case you cannot afford a lawyer one will be appointed for you and then asking if you need a lawyer appointed. Sure, if you're Bill Gates and you say yes, he might shut that down but the average person I don't think most jurisdictions actually investigate their means.
Ok, but I'm pretty sure that perjury is generally understood as being under oath and you aren't under oath when the judge is first reading you the charges against you and offering you the recourse of a public defender.
Although I suppose the court could hold you in contempt if it found you had the means and said you didn't. But I've never seen or heard of anyone being means checked.
Is your comment based on experience? It seems wrong.
All the search results (Findlaw, Avvo lawyer answers, etc) seem to be saying that you have to qualify financially, you have to submit your income and assets of your household under penalty of perjury (signed statement, not oath) and you may also be asked to get quotes from lawyers to compare against your means. I think the most you could say is that courts are so overloaded you might get away with perjury.
I qualified my original statement by saying "I think this depends on the state". Although now that I think of it, the laws in the states I know also say you can be made to pay back the costs if it is determined you could afford an attorney, however I have never seen anything done about it.
So I think you're right, it is perjury that doesn't really get anything done about it - I think based on the idea that if you had the money to get an attorney you would do it so anyone saying they can't get an attorney doesn't have the money.