If I find a record on Ancestry, for example, which has an FHL number, can't I look up that image using the FHL number?
You could try this:
go to familysearch.org - Search - Catalog and choose "film number" - Enter the number (not the letters "FHL") and the film series from which the document came will appear. Click on that and then scroll down until you come to the specific number for which you are searching. Click on that and the film should come up.