If there is (for example) exact date information where the gravestone photo shows only years of birth and death, I suggest contacting the person who created and/or maintains the memorial. First of all, you may learn that the memorial was created first (e.g., from cemetery records) and the photo was added later (so the person who created the memorial may not have known that he/she was giving more exact information than is on the marker - and also, they probably can tell you exactly where they found that information).
Second, I would not assume that the person who created the memorial just imagined what they entered, although it would be a good idea to ask questions. I have often sent people additional information relevant to a memorial (e.g., maiden name of a married woman, or place or exact date of birth or death). I make it a practice to tell them where it comes from (e.g., "Susan's maiden name was Smith, according to her children's California birth/death records," or, "the death index shows the exact dates of birth/death were ___"). But, many times the change to the memorial is made without adding the source, or any explanation for why it does not match up to the gravestone photo.
I agree that you should view the FAG memorial itself (as with any hint/abstract that references an actual document that is available for viewing). When I create a memorial that has information beyond what my photo of the gravestone shows, I always add the source in the "notes" section (e.g., "additional information from Kentucky Death Record" or "additional information from World War I draft record" or "additional information from California birth index" or whatever). Unfortunately, however, most people who create these memorials are not conscious of such issues, because they are not attempting to create genealogical records.
I agree that FAG memorials can be good finding aids, as I have had many cases where I was able to verify what the memorial showed once I knew what I was looking for (e.g., a maiden name, or a parent's or child's name), although going at it from the other direction (e.g., "what is this woman's maiden name") was an exercise in frustration.