Anomalous (? to me...) behavior using getJSON to make async REST calls in SharePoint 2013

Anomalous (? to me...) behavior using getJSON to make async REST calls in SharePoint 2013

Still accessing SharePoint 2013 lists using REST (_vti_bin/ListData.svc), and $.getJSON. I am seeing a behavior that I cannot explain, and was hoping someone here might have some ideas about what the issue is, or how I can (in the code) gather more information about what the issue is.

What is happening, is that I am able to retrieve the entire list, but I cannot retrieve just a single list item (which would seem much more efficient, once I know which list item I want...). To give a little more information, while respecting the NDA I signed:
this works --
      step1 = $.getJSON(" https://thesite/this/that/_vti_bin/ListData.svc/TheList", function(data) {...
but not this --
      step1 = $.getJSON("" https://thesite/this/that/_vti_bin/ListData.svc/TheList(15)", function(data) {...

The second version, that specifies one particular list item to return, simply returns nothing.

Both of these URLs work as expected when entered in the address bar of IE, so it would not seem to be an issue with the REST service. I have tried stepping through the code in Firebug, but the jQuery code is way too deep for me, especially given the time I have to complete my task... I can see where a variable is getting set to 'cancelled' and 'abort' in the ajax fcn, but I can't say why.

If anyone has ideas they would care to share about what the problem might be, or what I need to include in my .fail function to get useful information about what the problem is, I would be very grateful for any information that might help.

Thank you.