Yep, I think people who repeat this aphorism essentially equate programming with typing, or as you say just connecting existing bits together. Programming is the working out how to get a computer to perform some task, not just the typing, it's the algorithms, the performance balancing, the structuring, the integration etc.
Or theyre just picturing some CRUD app that needs to connect to a few APIs being made for a clueless exec who doesnt even understand their own business problem.
To be fair, a lot of programming does end up being just that.
Probably difference in the boundary of what programming entails too. Eg is coming up with the algo itself part of programming or only the writing the implementation part after the algo is clear.
The first is hard, the second much less so.