The content that is available is controlled by content provider.
I'm guessing that previous episodes are available, but only for a fee (there again controlled by content provider).
Why can I log into the FiOS site, click Watch FiOS, search for Broadchurch and be presented with four episodes from which to choose. Clicking on any one of those episodes takes me off-site to the BBC America page, where I am prompted to select a provider in order to watch. I choose FiOS by Verizon and I'm presented with another login form for FiOS, into which I enter the requisite information and the page attempts to log me into FiOS (again). Shortly thereafter, I'm presented with the message that I need to subscribe to FiOS. WHAT? If I can't watch the displayed episodes at all at BBC America's site (to which FiOS is redirecting me), WHY PRESENT THEM ON THE FIOS PAGE AT ALL???
This is the same flow when trying to use the individual networks' mobile applications, such as HBO Go and the like. Something is either broken here with FiOS, or FiOS is intentionally blocking this functionality, even with these networks providing FiOS as an option in their provider screens.
I only reached the point of plugging my laptop into the TV because of the frustration and utter futility of trying to access the program through the standard On Demand functionality of the FiOS media client/server.
I was able to watch the first episode of season 3 of Broadchurch on the TV through the DVR, which for some reason offered that as an On-Demand option when setting up the series recording, but *only* that episode. The episodes recording or scheduled to record on the DVR are all listed as episode 0; where this is a series that demands watching in order from the beginning, not knowing which episode is recording/recorded means we can't even watch them.
We'll probably end up just waiting for this to end up on Netflix, thanks to this utter confusion and incompetence.