As I said, if this were really true, there would be evidence of people using it to express thoughts that are too hard to express by other means. But in reality, people who think in APL just don't seem to be on the forefront of published algorithmic thought.
It might be helpful to contrast APL with nonstandard analysis, a mathematical tool of thought for doing rigorous real analysis more easily. People have proved new and useful results in nonstandard analysis, and the fact that these results were first proved in nonstandard analysis is at least some evidence that nonstandard analysis served as a real tool of thought to produce those results. (To be fair, the idea that nonstandard analysis was an essentially tool in these proofs is controversial among mathematicians. But there is at least the hard fact of the results being proved first by this means.)
So, if smart people are able to use APL to push the boundaries of algorithmic thought, we'd expect APL-ers to have that sort of achievement to show for it. But we don't see that. After pre-existing thoughts are translated into APL's logography, there does not seem to be any demonstrable enhancement of the ability to reason about algorithms. Or maybe there is some enhancement for that individual person, relative to their abilities without APL, but it does not seem to cause that person to rise above the general human level of algorithmic ability.
"APL as a tool of thought" seems to be a beautiful theory whose predictions have not met with reality.