True, but there are some extroverts who need, or desire alone time a lot less than others.
I am quite balanced in my E/I divide but I don't think anyone who has ever known me, especially in social situations, would ever question the fact that I am an extrovert, well, cause I am.
But, the mere thought of constantly, or frequently, being in the company of others exhausts me. Such is not the case for some extroverts.
My ESTJ sister and ESFJ mother not only need, but desire and prefer damn near constantly being in the company of others. If they can help it, the only time spent alone would be while taking showers/baths, and sleeping, I guess. My mother requires a daily down time consisting of a thirty minute bath while my ESTJ sister uses driving as a time to "sort her head", but other than these two exclusions, they just don't operate well when by themselves.
So, there are plenty of extroverts who thrive in the constant company of others, while there are others who thrive in a happy balance between being by themselves and being with others.