You have to understand that fatty liver is a symptom, like a headache, that can have a dozen different causes. The most well known is alcohol abuse, but various drugs and diseases can affect the liver too.
If you've been diagnosed with a fatty liver your GP should be pursuing the cause, and at least ruling out some of the more serious options. If you've had a scan them they've obviously ruled out tumours and other obvious physical causes, and if you're not a heavy drinker/alcoholic then it's not likely to be that. The next step is to review your medication - statins, some pain killers, some vitamin overdoses and herbal supplements as well as some other drugs are known to have an adverse effect on the liver. Diabetes is a known cause of fatty liver, but autoimmune liver disease is on the rise and can lead to liver failure if not treated.
Not all GPs will go this far though, and take the attitude that if it's not causing you any problems then they're not going to dedicate time/money/effort to finding out the 'why'. But in my (educated but not professional) opinion it's worth a blood test to rule it out, because the only option for treating complete liver failure due to autoimmune disease is a transplant.
