Low-sugar and no-sugar jams can be shelf stable without being refrigerated provided the filled jars have been processed in a boiling water bath for at least ten minutes. (Jars of course will seal without this step, however temps reached during process in a canner are high enough to kill mold spores or bacteria that the jam may have come into contact with during the short process of moving it from pot to the bottles. Granted full sugar jams are more likely to maintain color longer and are less prone to discoloration, but added sugar isn't absolutely necessary to preserve the jam. (Yay for diabetics and people cutting down on sugar!
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I think the issue with my strawberry jam was more discoloration than mold and I don't think I cooked it down long enough, which would have concentrated the natural sugars in the fruit as the moisture content was boiled off.
Btw boiling the filled jars in a water bath canner for ten minutes also eliminates the need for adding wax discs and it also provides a stronger seal.