A likely explanation is that the communications director (or the people informing her) wouldn’t know to distinguish between Signal the app, and a Signal compatible app that is nearly indistinguishable from Signal. A lot like Kleenex is a common term for tissue paper regardless of brand.
When the leak was first revealed, there was loud speculation about the legality of government chat messages being set to auto-delete. This additional revelation, about the use of TeleMessage, shows that someone with a security background has actually thought about these things. It makes perfect security sense to archive messages somewhere secure, off phone, for record keeping compliance while ensuring that relatively vulnerable phones don’t retain messages for very long. It’s also an easy explanation for why such an app was created in the first place. There is an obvious market for it.