In regard to identity, that's an awfully human thing to assume. If there were an intelligent, alien observer, the chances that their biology, social structure and interactions, not to mention expectations might be so radically different (alien) that they would really have no idea what to make of what they were seeing except through the lens of their own experience. If there are humans who have trouble telling members of another human race apart, as Europeans in various parts of the world do with Asians and vice-versa, then I doubt that alien observers would be sensitive to "how different we all are."

As for advertising not being similar to evangelism, I contest this. There is advertising for things where teaching is not only implied, it's the product being sold. As for the lack of large and frequent gatherings, well, if the observer came from a species and culture where large, frequent gatherings do not imply religion, then that would mean nothing. No religious texts? There are many religions that began as oral traditions. Why would an outside observer assume that humans would deviate from that? Perhaps the oral tradition is sacred and cannot be put on to paper. No grand structures? Religion being much more complex than fast-food dining? Who knows. That could be explained in any number of ways, including humbleness before god/s or frequent, prayer in small groups rather than large congregations for whatever reason.

The point is, how would an outsider look at things, not how would you as a human look at things. Heck, they might not even realize we are sentient at a quick glance. Perhaps the observers would be so far beyond our mental capacity that we'd appear very much to be animals, albeit a higher order of other animals on the planet.