[Piranha]

I don't have a concordance here, but I wonder whether a search of the Torah's use of the word "am" would show it used to refer to any other nations (am prizi, am hitti, etc.)

[avitot]

your not incorrect in saying am can mean people in the generic sense, but in a language of limited words they often have more than one definition.
Dvarim:
Shoftim 20 ,17 the seven nations ;hittites,amorites,canaanites etc are referred to as haamim.(plural for the nations). sometimes goy is the term used for nations.