I'm sorry to hear about the stage IV diagnosis. It is far more likely that the PET scan picked up what the other scans did not (rather than rapid growth). I am a PET scan believer as my mets were only diagnosed via PET.
Being confirmed as stage IV means that he will get the most aggressive treatment and the most comprehensive surveillance (scans + bloodwork). While its tough to hear it is far better the sooner Stage IV is identified, rather than being incorrectly staged at III.
For both liver and lung mets there are treatment options which have led to long term NED in a not insignificant number of patients. While it is devastating you are at a point where there is every reason to hope for a good outcome.
Hope that helps
AT