[mod note: I'd already sent this in when Mark Robins' reply and
FAQ came in. I think much of my reply to Ellen is now redundant,
but I'll leave it here anyway as a more direct point-by-point.
-- Shal
]

Ellen,

Now as I understand Grouply.com, if I posted on a group where
some other member is also a member of a Grouply.com group, then
my posts in a Yahoo group’s Archives would show up in Grouply
even though I am not a member of any Grouply group.

There is no such thing as a Grouply group. They are more akin to an enhanced email service (think gmail, but with features tailored to make reading Yahoo Groups faster and easier). In particular, Grouply will only show your posts in a group to other members of that group.

Grouply.com is different.  It doesn’t seem like my member would
have to actually do something to forward or re-transfer the
Archives but their membership under and disclosure of their
Yahoo ID is sufficient to initiate this transfer without the
permission of Yahoo group owners and easy member posting in a group.

It is true that accessing messages from your Yahoo groups through Grouply is simple. One registers for an @grouply email address and provides them with your Yahoo credentials. Grouply takes care of setting your memberships to the @grouply address and setting your delivery to "Individual". From there you choose what level of digest you want Grouply to create for you.

Grouply's belief is that they or their subscribers would no more need a group owner's permission than gmail would. Grouply is merely delivering messages which their subscriber already has permission to read.

... but is Yahoo going to pursue a TOS outside the Yahoo group system? 

I don't understand the premise of your question.

In essence Grouply has an unauthorized copy of SewEverything
Archives to use as they see fit. 

As would gmail, if you have a member with a gmail address.

Neither Google nor Grouply can legally use those copies as they see fit. If they published them that would definitely be a Copyright problem. Grouply asserts that not even their own employees have access to the content of group messages (heh, except for those groups that particular employee might be a member of); any breach of that commitment could take down their whole company through loss of reputation as well as through customers' breach of contract suits.

...  What about the member who was banned and their best friend
who didn’t let anyone know but has joined Grouply.com and now
the banned member still has access to the old group info? 

Nope. That's one of the things they do with their subscriber's Yahoo credentials: verify their My Groups list. The banned member would promptly lose access to the group through Grouply as well.

Notably this sets them apart from gmail or for that matter from my hard drive: I'll never lose my copies of messages from my groups merely because some future mod decides to remove me.

I do have a problem with what I post showing up elsewhere
without my consent, any way to find out where it is, who is
using it, having no way to remove it from where I don’t want it
to be and having no recourse when someone else has control of
what I posted where I wanted it in the first place.

Then stop posting, because there's no way for you to control any of that now. Sometimes your posts show up at my work, sometimes in my home office, sometimes in my bedroom(!). Wherever I check my email. I have reason to know that some of your posts were spotted in the Caribbean a few weeks ago...

I'm being a bit facetious, but with a point. All of the members of your various groups are causing copies of your messages to appear and be stored in all sorts of places. None of that is a problem unless one of those members makes a copy available to someone else (and even then you may have to argue about circumstances).

Except for the word blog, I see no difference in my group
messages showing up unauthorized on anyone’s blog or
over at Grouply.com.

There's a HUGE, HUMONGOUS, SIZE-OF-THE-UNIVERSE difference: blogs are posted for all the world to see. They are effectively a form of publication.

Grouply is an access service that allows each specific subscriber to access messages from those specific Yahoo Groups of which that subscriber is a member. I do not believe that constitutes publication in any way, shape or form.

Or, logically, if it does then so does gmail, MSN/hotmail, Verizon, AOL, Comcast and every other service, including Yahoo Mail, that I might use in lieu of reading messages directly from the group's site at Yahoo.

Content showing up from my group without my permission and the
permission of my group members after a group member joins
Grouply.com is IMO a TOS.

I guess the key here is "showing up". If I could through Grouply access messages from groups of which I am not a member then I'd agree with you. But as long as they operate within their policies I'd say no.

Unless Yahoo is going to make an exception for Grouply.com .... 
Grouply.com group is not authorized to Archive any Yahoo group
Archives without owner AND member permission for those messages. 

I don't think any exception or authorization is needed. Grouply acts as a delivery agent for its subscribers. Those Group members that subscribe to Grouply have permission to access those messages, there is no need to authorize any specific service by which they may accomplish that access.

-- Shal