Being on your parents health insurance has nothing to with you being a dependent.
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
The opposite may not be true. Your parents insurance plan may require you to be a dependent. But my understanding of Obamacare is that they have to accept you thru age 26, regardless of dependency.
