Should the stores maintain their own state and have the ability to call network and data storage services in doing so ...in which case the actions are just dumb message pass
The stores should do everything, including fetching data, and signalling to components that the store's data has been updated. Why? Because actions can then be lightweight, disposable and replaceable without influencing important behavior. All important behavior and functionality happen in the store. This also prevents duplication of behavior that would otherwise be copied in two very similar but different actions. The stores are your single source of (handling the) truth.
In every Flux implementation I've seen Actions are basically event strings turned into objects, like traditionally you'd have an event named "anchor:clicked" but in Flux it would be defined as AnchorActions.Clicked. They're even so "dumb" that most implementations have separate Dispatcher objects to actually dispatch the events to the stores that are listening.
Personally I like Reflux' implementation of Flux where there are no separate Dispatcher objects and Action objects do the dispatching themselves.
edit: Facebook's Flux actually fetches in "action creators" so they do use smart actions. They do also prepare the payload using the stores:
https://github.com/facebook/flux/blob/19a24975462234ddc583ad740354e115c20b881d/examples/flux-chat/js/actions/ChatMessageActionCreators.js#L27 (line 27 and 28)
The callback on completion would then trigger a new action this time with the fetched data as payload:
https://github.com/facebook/flux/blob/19a24975462234ddc583ad740354e115c20b881d/examples/flux-chat/js/utils/ChatWebAPIUtils.js#L51
So I guess that's the better solution.