Well certainly after a service has been done the car will perform more efficiently and better, hence the reduction in fuel consumption. But to say that it gets better fuel consumption due to age alone is false; if any, it will get worse if nothing has been done for maintenance. Older cars will need to eventually have the valved adjusted, the timing checked, sparkplugs replaced, etc. Newer cars will have more sensors so if these sensors go bad it can send bad feedback to the computer which results in changes caused by faulty sensors. For example, mass air flow sensors can get bad especially if used in conjunction with K&N filters (the cleaning solution on the filter can ruin MAF sensors). Or another, oxygen sensors need to be replaced eventually.

Once the bad parts have been replaced as in a PMS or maintenance due to bad parts, then the car will perform better.