This is demonstrably false to anyone with one of these devices. I can page over to my podcast app that I used days ago and find it is exactly where I left it.
Not sure why the downvotes, it's largely true. Almost every non-techie I encounter in real life incorrectly uses the term "memory" to mean storage space.
Is it really that incorrect? Flash memory is persistent storage. Memory cards used to be how game saves were stored on consoles. The M in ROM stands for memory.
So it seems like we're using the term memory too narrowly, rather than them using it incorrectly.