OK, I believe I have answered my own question, and confirmed that in this case you would NOT want to Join the data as the warning prompt suggests b/c you wouldn't be able to tell your properties apart anymore. (There isn't a column in the table identifying each property by name.)
I think the reason Tableau believes these are all from the same data source is that they are from the same Google Analytics Account. I am guessing that most people would not want to join data from the same GA Account... it would probably only make sense to join the data if they were from the same GA Profile. i.e. the most granular level in the account heirarchy (Account > Property > Profile). At the Profile level, you would indeed be pulling data from the same source, so it would potentially make sense to Join different tables you've extracted.
Oh, and here's my successful Visits trend -- using the Visits metrics from the three separate data sources.
Same problem here,
what did you do that it worked?
Blending does not work because of the same data source for primary and secondary data source?