The health insurance is not relevant when determining if they can claim you as a dependent.
If you were a full-time student in 2018, they may be able to claim you as a dependent if you did not provide more than half your own support.
If you were not a full-time student, different rules apply. If you earned more than $4,150 from your job, they cannot claim you as a dependent. It sounds as if this is the case for you, so you will NOT check the box indicating someone else can claim you as a dependent. You will claim yourself, as they are not eligible to do so.
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