Hriston
Dungeon Master of Middle-earth (He/him)
Roleplaying is a general category, like money. Trying claim that there is only one degree of roleplaying is like saying that there are no denominations of money. Playing the bare mechanics and nothing else is like a dollar bill. Not caring about mechanics and just going with story over everything would be like a one hundred dollar bill. Everything else in in-between. That doesn't mean that the $100 is the only way to play, or that the $1 is bad, but there are greater degrees of roleplaying than what you describe above.
Your metaphor is off. The way to have a greater degree of role-playing is to play RPGs more often. If you only play once a year, that's like having one dollar. If you play one hundred times a year, that's like having one hundred dollars. The differences you're describing are differences in play-style. They are all equally role-playing.
A statement doesn't achieve one true wayism unless that person is telling you that you have to do it their way.
Then I'm sure you'd have no problem agreeing that "playing the bare mechanics and nothing else" in no way diminishes the amount of role-playing you're doing compared to "not caring about mechanics and just going with story over everything". Since I don't have to do it your way for it to be role-playing, then one play-style can't result in less role-playing than the other.