I just took our gmail account off moderation to see if i could replicate things - but still it seems to be working ok with me.
Here is what i did in case it's helpful to compare notes:
1- I took the gmail off moderation
2- i switched it to all messages
3- I sent a post from the gmail account via web to the group and i got 1 copy of the post in my gmail inbox from "me" and there was one in my sent folder too on gmail (gmail interface)
4- I sent an email via gmail email to the group and i got 1 copy in my gmail inbox and one is in my sent mail.
I didn't try it when on "digest" or "no email" as I think it's not supposed to work in those instances as those settings override that..?
And in iphone mail it also behaved as it should with only one copy delivered.
And just in case it's helpful info: I don't forward my gmail to a mail client and don't have it downloaded in a mail client so can't help with that but do recall reading about duplication issues elsewhere in certain mail clients with gmail - can't recall context maybe a POP and forwarding issue happening concurrently - prob. not case here...
Sorry! I was wishing I could have replicated and help find a clue - but seems to be working fine for me.