Even if this was true in 2013, when this article was written, the more accurate answer today would be "it depends".
In Rust, there are multi-threaded async executors implementing M:N threading (e.g. tokio), where M asynchronous tasks are mapped to N operating system threads. So when you await, the rest of the function may very well run in a different OS thread.
Swift also has async/await, and like tokio it uses multiple threads to run concurrent tasks in parallel (therefore using multiple OS threads).
Scala's equivalent to asynchronous tasks are Promises, which can also run in parallel, as I understand it.
Kotlin doesn't have async/await, but it has a similar concept, coroutines, which are basically a superset of asynchronous tasks. While Kotlin's coroutines are single-threaded by default, there is a multi-threaded implementation, enabling truly parallel coroutines.
Go also uses coroutines (which it calls "goroutines"), which can use multiple threads.
C++ will soon get coroutines as well, which support multithreading to run coroutines in parallel.