Yeah, the whole thing assumes that the aliens would be using a communications technology that:

1. we can actually detect it with our current technology.
2. would still be identifiable as communications by completely different alien species.
3. wouldn't just become a garbled mess by the time it reaches its destination.

We've had radio technology for about a century, vs the 10,000 years or so of human societies existing. Even as recently as 200 years ago, we'd probably be expecting the aliens to show up on horseback with a handwritten missive to be read to us. We make a lot of assumptions that they would use radio waves to communicate, and would beam radio waves at us, when we could very well be using technology that these aliens abandoned for more advanced communications technology centuries or even millennia ago.