Does Redshift Indicate Mutual Movement Between Distant Galaxies?

[aerogurl2]

I don't understand whether this is true or false. It goes like this:
if a distant galaxy has a substantial redshift ( as viewed from our galaxy) then anyone living in that galaxy would see a substantial redshift in a spectrum of the Milky Way galaxy.

I know redshift is when the object is moving away from our galaxy, then wouldn't we see that galaxy moving away as well? am i offtrack??

 

[Mindscrape]

Yes, we would see the galaxy moving away from us too, but what does that have to do with the question? The question is hinting at frames of reference.

Do you know about special relativity and the doppler effect?