Communication isn't going to try to perfectly mimic natural sources, and it won't try to hide in the background. It's reasonable to say that we won't be able to understand any sensibly coded message that wasn't intended for us, but that doesn't mean we won't be able to see it.
The biggest problem is detector size. Even if we assume a best case scenario, and there is some friendly alien race out there who has pointed a beacon directly at us, intended for us to detect, these aliens would assume a certain level of technical competence on our part. The easiest way to make a really huge collecting lens for a telescope is to use the gravitational lensing effect of your own star, and put a secondary lens somewhere in your local oort cloud. Our hypothetical alien friends might assume that if we are capable of building radio telescopes, we're also capable of putting those telescopes in a sensible place in our local system, and as such might be transmitting on very low power.
A gravititational lens telescope would be significantly more sensitive than anything we can build on Earth, by several orders of magnitude. The same gravitational lensing principle can also be used to send signals at very low power between stars.
Our problem might just be that we are assuming aliens will be hugely wasteful with powerful signals, when any sensible technological civilisation goes the low power route.