In defense of the parent, anyone that practices a trade (singer, actor, artist, programmer, developer, engineer) typically doesn't identify themselves as one of the aforementioned titles unless they get paid to do so. Now, mind you, that doesn't mean in the most traditional sense that lack of monetary reward/success doesn't disqualify their skill but, in this world, it certainly validates ones work/interest.
To make my point, society typically doesn't label someone that can sing a 'singer' unless that is their profession and they get paid for it. Even though I script and do 'some' programming, I wouldn't dare call myself a programmer.
I believe that one shouldn't get too hung on titles. For me, at least, I find a sole definition limiting because there isn't a single title that describes everything that I'm good at, however, there is a single title that describes what I'm good enough to get paid for.
So I must disagree - one is an artist if you make art that is meaningful to yourself. I have known many artists over the years, and most of us just quietly do our own work for our own reasons. I will not go so far to accuse people who do it for society's reviews and recognition to not be artists - that would be dismissive of their own goals. But artists have varying reasons for doing their work, and trying to define a "true artist" is going to invalidate someone unfairly.