Well... that's the question.

It doesn't matter if you're actually a citizen. If the government refuses to admit your citizenship, how do you get them to admit your rights apply?

I would love to get more clarification on this as well. It seems to me that if there is doubt about your citizenship, we should lean towards better safe than sorry and just grant you a lawyer, period.

The US justice system is (ostensibly, if not always in practice) based on the idea that protecting innocent people is more important than punishing guilty people. If you're being tried to see if you're a citizen, I would prefer we assume you're innocent until proven guilty and grant you a lawyer.

Is the reality as bad as people are suggesting? Is there some kind of reasoning behind this?

The Bill of Rights isn’t just for citizens, most of it (including the 6th amendment) applies to anyone on American soul.

Legally I have no idea what the government claims applies or does not, but reading the declaration it seems pretty clear that the founders had the still-radical notion that most/all of these fundamental rights apply to all people ("men", in the text, and "[white] men" in practice). There wasn't even such a thing as "American" when it was written.

If the US thinks the bill of rights should only apply to citizens of the US, the US is morally bankrupt.