Hardware and performance

Hi Laura

Your original question,
> But as it's a standard open license LMS, built on PHP - why a server, with a full SQL/PHP database could not support Moodle?

The reasons have nothing to do with licences, they are techncal. The first one,

> "The Moodle script most likely won't work as the application requires a storage place outside FTP root, which is not possible with us ..."

They mean the the "moodledata" directory: http://docs.moodle.org/en/Moodledata_directory

It has to be outside the _HTTP_ root http://docs.moodle.org/en/Installing_Moodle#Create_the_data_directory , not FTP root as your provider writes. Still the net result for you is likely to be the same. I haven't tried it recently, it may be possible to go ahead keeping the moodledata withing the HTTP root, but a malicios person can destroy your site through the web.

The second one,
> "... and uses Innodb and MyIsam as an engine if nothing else is available and will probably have problems with our server."

Innodb vs. MyIsam is not relevant for a test site. Probably they mean that Moodle requires more ressources than they provide.

In the OP you said:
> am supervising a couple of undergrad projects developing Moodle.

Do you mean developing Moodle code further or developing content and doing the normal administration? For the latter, I remember there were even free offers in this site. Try the search facilites http://moodle.org/mod/forum/search.php?search=&id=5 and http://moodle.org/public/search/