In the same sense, I "have a PhD in AI". You have a PhD in "what could be said to be the Landlands problem itself". It happens.
In my experience there is a strong correlation between depth of understanding and being able to communicate a topic effectively. I have encountered many technical papers that drape simple concepts in needless complexity. My area of expertise is software design and it's usually the least skilled people that produce the highest complexity. I find there is a lot of value in solving things in a way that is easy to understand.
If every step clearly follows from the prior steps it’s rather immaterial how long the proof is. Similarly a short proof with enough rabbits can achieve a kind of incomprehensibility.
What's a "rabbit"?
I claim that I would be able to explain some rather deep results from my area of mathematical expertise quite effectively. But for the ordinary person to understand my explanations, we would have to start with a full-time course about elemetary basics that lasts for quite some months.
On other words: just because you are able to communicate a topic effectively does not mean that the other side has the necessary background knowledge to understand your good explanations.
However here we are not talking about laymen, we are talking about people with PHDs in related or exactly this field. If they can't understand it, who is left?
In particular in mathematics, research areas are quite isolated from each other, so even for a people from a related (sometimes even from the same) field, it typically takes a very serious effort to gain the necessary knowledge to understand a proof. This is also a reason why paper reviews take so much longer in mathematics than in many other academic disciplines.
I'm asking this because in my field of expertise it's a common correlation, that the more complex and arcane a piece of code is, the lower the chance is that issues will be discovered during review. In addition the chance of issues grows superlinear with complexity, as more control flow and invariants needs to be tracked in error prone human minds.
I can explain stuff to an 8-year old child, but a very long part of my explanation will be about bringing the child "from zero to graduate-level knowledge" in mathematics.
The solution to explaining stuff to an 8-year old child is thus not by making the material sufficiently stupid to make it understandable to a typical 8-year old, but to make the 8-year old sufficiently smart and knowledgeable to understand the topic.
Not unlike IT, medicine, or parts of software development.