This is absolutely correct but still not the whole story. Recycling for glass and aluminum and steel can be done essentially infinitely creating a largely closed loop (though for glass in particular we really need to return to our old reuse practices). By using the same language for plastic as we do for better recycling methods we still make plastic recycling sound better than it is, even when reduction and reuse are emphasized.
I imagine that goes the other way, too: by conflating the scam of plastics recycling with recycling in general, some people are probably discouraged from recycling anything at all, including aluminum.
Plus the whole system was created with the idea of getting people used to recycling so when better, more efficient forms of recycling came into use, people would already be recycling.
Too bad that whole "better, more efficient" part never really happened.