Besides Extendables, there are 2 alternate options:
Adobe Bridge/Bridgetalk
Can't say for specific versions of the Adobe suite, but if you can use or have Adobe Bridge/Bridgetalk, you can make use of Adobe's cross app communication and HttpConnection class available to Bridge (as per the SDK doc), and have InDesign call Bridge to make the HTTP request and pass results back to InDesign.
I don't have specific example for InDesign, but here's some meant for Illustrator. I would assume it would port to InDesign easily.
https://gist.github.com/daluu/2d9dec72d0863f9ff5a7
https://gist.github.com/mericson/6509997
Make web service calls externally and interface to ExtendScript
Adobe's scripting API engine is not strictly ExtendScript/Javascript. You can also use the script API from COM/VBScript (on Windows) or Applescript (on Mac), which execute external to InDesign but interact with InDesign via the API.
For Windows, by COM, I mean any language that supports COM, so it's not just the default VBScript (can be Python, Perl, PHP, Java, .NET, even Microsoft JScript - their version of Javascript for command line/desktop/etc.).
Using the script API on a different engine, you make the web service call externally from other language (VBScript, Applescript, etc.) then pass the results into the ExtendScript via the script API call (in COM/Applescript) of application.doScript('ExtendScript code snippet here') (or doJavascript) where for ExtendScript snippet, could be a short snippet that uses ExtendScript includes to include actual JSX file then call a ExtendScript function/method, passing it the web service results as arguments.
An example of this technique (not covering the web service call portion) is described here in some of the solutions:
Is it possible to execute JSX scripts from outside ExtendScript?