Semi-off-topic rant incoming, but hard disagree on this one. This is a really weird statement that is commonly used for the opposite of what it actually means (although not in this case). I don't enjoy syntactical discussion, e.g. whether I used the wrong sentence structure or whatever, as long as the meaning is clear. But discussion on "the meaning of words", i.e. their semantics, is absolutely necessary in many cases, here about whether we use the same definition of this idiom. You can't properly communicate without that, so if you don't discuss semantics where appropriate you are talking at each other instead of with each other, despite using the same language.

but I’m saying that we don’t believe in the problem.

Case in point here, you are operating from your intuitive definition of the head-in-the-sand idiom which doesn't fit the situation at hand, I'm operating from the Merriam-Webster definition which does fit the situation at hand.

Just to be clear, I don't intend any judgement here, just saying it fits that one specific definition of this idiom, which is why I quoted it originally.

As stated in the grandparent of this comment I can agree with many of your examples, so I understand your revulsion of categorising your behaviour as sticking your head into the sand. But to people who recognise and acknowledge the problem, unlike you who recognises but doesn't acknowledge the problem, you are sticking your head into the sand.