>Mean and average are synonymous. He was precise and correct in his terminology.

No, he wasn't precise and it isn't synonymous.

First words from the wiki:

>In ordinary language, an average is ...

Ordinary language, as used by the wiki, means "colloquially", which is not precise mathematical/statistical/scientific language.

Later in the wiki entry, we have this:

>Depending on the context, an average might be another statistic such as the median, or mode.

...which blows your assertion of the precision out of the water.