Profitable does not mean 'making more money than you could otherwise', profitable does not mean 'worthwhile', profitable does not mean 'sustainable without ones founders.'
Profitable means making a profit. End of story.
This is a petty, semantic issue. if a company is making $50/month in profits, then the issue isn't that they're calling themselves profitable, its that they're only making $50/month.
It's really a question of how time factors into your accounting. If you're spending 10 hours to make $50, then it's tough to claim that as a $50 profit unless your time is worth less than $5 an hour.
Of course there are cases in which your time is worth less than $5 an hour (you don't have any other prospects for making money). Or if you enjoy what you're doing it might only be 1 hour of "work" with 9 hours of enjoyment. The point is that completely ignoring time spent is just bad accounting.
Profitable means making a profit. End of story.
This is a petty, semantic issue. if a company is making $50/month in profits, then the issue isn't that they're calling themselves profitable, its that they're only making $50/month.