Well, I heard back from Ryan in Support:
In reply to:
I'm sorry for the confusion. Google Checkout is _only_ available when a balance is due. If an account shows a balance of $0, then Google Checkout won't be shown on the Make Payment page. Since registrations and renewals must be pre-paid, indeed, Google Checkout is not an option for renewal. The reason it is available for signups is that the balance for the hosting/registration is assessed prior to activation and thus there will be a balance due and then Google Checkout is a possible payment option (you have to pay before any registration or renewal if it isn't covered by a hosting plan's credit, in other words). You didn't provide a link to a forum post, but you may want to pass on this information and wiki link:
http://wiki.dreamhost.com/Payment_methods
and indeed, the wiki does mention that Google Checkout is only an option if you have a balance due, and as Ryan says, this means that Google Checkout is not an option for renewal.
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