You're right, the article claims OP had 1099 earnings of $9.34/hour assuming expenses of $0.51 per paid mile. But then also goes on to note that other driver's expenses were more like $0.70 per paid mile.
I wonder if she amortized that $100 of tire damage in that $0.51 / mile! Also, what about the unpaid miles getting to a fare in the first place, or getting back home after a fare takes you off the beaten path? I think it's extremely difficult to fully account for all time and expenses in that line of work. Finally, subtract another 7.6% off the top for 1099 vs W2.