Talitha Robinson-Russell and Carlos Russell sat with 'Today' to talk about the case -- which has been shrouded in mystery ... and which has come under public scrutiny due to the scant and inconsistent details following Carlee's 48-hour disappearance.

Despite the growing skepticism ... Carlee's family is standing firm she was abducted ... echoing her story she escaped her abductor.

Her parents say she was in a bad state when she arrived at their house Saturday night -- and she's disturbed by people questioning her honesty.

As far as any other details, however ... the Russells are refusing to elaborate, citing an ongoing investigation.

Some feel like the facts of the case aren't lining up ... not to mention the police apparently having left out some pertinent information in terms of what they knew about her recovery and when. As we reported, first responders were discussing Carlee possibly having been located at a local motel in town ... but in their statement, they totally omitted that.

There are also questions about this alleged child Carlee claimed to have seen on the side of a highway the night she vanished. Police say they received no other reports, besides the 911 call from Carlee, of a missing child.

So if there is, in fact, an abductor and a possible kid at risk -- why haven't the police issued any kind of alert to that effect? That's what people are asking.

Fair queries, and yet ... still not very many answers.