Progressive inferential is a variant of focal inferential, denoting an action beginning some time before the time of reference,
and continuing presumably for some time after it,
and expresses that the knowledge of the fact is the result of the speaker having been told of it,
very often indirectly, by hearsay. That knowledge is in general deemed as dubious.
Other possibilities are that the knowledge is the result of direct narration (but then also seen as dubious), or even of dreams.
The temporal distinction between a past and a present state, event or action is not marked grammatically,
the tense must be decided from the context.
It is used mostly in written language, and is typical of a factual or newspaper style.