MInd explaining this in clear terms?
"NB the primary site for the domain is on another server)"
On a 'subdomain'? What is the subdomain? and how does that compare to your config.php file variables? (even if HG support says it's correct!)
You've not mentioned what plan you have with HG - am assuming 'shared'. Have you read:
https://support.hostgator.com/articles/hosting-guide/hardware-software/php-5-3
"Things to Keep in Mind
If you are using a custom php.ini file that references PHP modules that are not available with PHP 5.3, your site may not work. Either remove the custom php.ini file (which will cause the server to use the default php.ini file for PHP 5.3), or create a php.ini file that is compatible with PHP 5.3."
As far as HG Support comment about 'known issue', obviously, it is not or one would have found something in these forums related to the issue. The extension mentioned is not the only required extension:
http://docs.moodle.org/22/en/PHP#PHP_Extensions_and_libraries
And just a warning ... with shared plans there are caps/limitations (those can be found in HG forums/information) so if the plan for your Moodle installation will require higher than those caps/limitations, HG is not the place to host on shared plan.
'spirit of sharing', Ken