The Dutch page http://www.geni.com/gedcom states that you can do a forest export on any profile you can see ("Tip: U kunt voor elk profiel een GEDCOM-bestand exporteren, als u de rechten heeft om de stamboom te bekijken.")
The English page states the same:
Export Forest including connected inlaw trees (up to 100000 total individual records) A Forest export may take several days to complete. Tip: You can export a GEDCOM file for any profile where you have permission to view the family tree.
If the page is correct than the program is incorrect for blocking free users from exporting the trees for other profiles then their own profile. Otherwise the wording on the page is incorrect for free users.