Run many CentOS servers but not any remotely hosted thus have full control over config and no restrictions. Your hosting provider does have restrictions on a shared hosting server and is in conflict with Moodle's requirement to have moodledata NOT directly accessible via web browser (ie, NOT in document root).
Document root on your hosting system is:
/var/www/vhosts/mydomain.org/httpdocs/
Question:
** Can you set document root for:
/var/www/vhosts/mydomain.org/httpdocs/moodle/
Then, moodledata folder can reside in httpdocs and their setup shouldn't complain - and moodle installation shouldn't complain either.
BTW, your hosting provider is a little incorrect in saying it's an installation error and they *can't* do anything about it. It is an error the way they have configured their shared hosting for Moodle from which it appears they will make no exceptions.
To be totally honest, if one has issues (and no cooperation from provider), will there be other issues in the future? Consider that Moodle 2 may NOT run very well on some shared hosting solutions. So, one might have to 'shop' for a provider that can and does setup systems that support Moodle 2. My 2 cent opinion, of course.
'spirit of sharing', Ken