Your definition of a public line may not be accurate.
Do you think Crown Prince used your version of a public line when he ordered the hit that Gina Haspel may or may not have said was recorded.
I don’t know anything about the Clarion Project. Some or none of the following story may be true
https://clarionproject.org/revealed-khashoggi-was-a-qatari-asset/
But is shows exactly why a Head of State would inform another Head of State.
Btw, Imam of Peace is hot and heavy on Qatar undermining the US including through Ilhan Omar. There is a current law suit over the ordered hit of someone that may bring out more details.
If Turkish Intelligence were to have “intercepts” of the call (as stated in the article) then I’d say it wasn’t a secure line. Now I don’t believe that but that was my point.