I'm pretty sure that in advanced IMAP settings you can set it to delete or archive from the actual GMAIL website. Sooooo... You're both right! 
Also is there any way yet to star/flag emails? So annoying. How about to COPY instead of Move? Then I could just copy them to the stared folder because moving would be Star+Archive, which I don't want.
Also is there any way yet to star/flag emails? So annoying. How about to COPY instead of Move? Then I could just copy them to the stared folder because moving would be Star+Archive, which I don't want.