By the way it looks like Github API sucks a bit with authorizations, but I still don't see why libcurl handle them automagically while the FCL web client not.
And how many code does libcurl need for that... then compare that to your one-liner.
Do you really expect .simpleget() f.e. to automatically redirect, handle client certificates, play animations etc. for you ?
That's why i said use curl as your guide and let it do some verbose logging to see what is required to retrieve that url. Then figure out if SimpleGet() is able to do that (as i said, i don't believe it is). so ditch the simpleget() and use TFPHTTPClient exactly in the same way that curl does. In case that is failing, then there is valid reason to suspect TFPHTTPClient failure/bug (or missing feature).
edit: ah, ic Dimitrios already figured out the exact reason for you