Not directly, it doesn’t, but you did establish two separate sets of sitters: those who pay premium, who might be more responsible and those who don’t, who might not be as responsible.
I am a premium member, so no offense taken but my decision to pay for premium has nothing to do with my reliability and I don’t think it has any impact on HOs. The “added benefit” of premium membership is for the member who has chosen that tier, not for the other party.
I hadn’t given it much thought but you may be right there. THS do list the “premium badge” as a benefit associated with premium, perhaps indicating a higher group who should be able to easily identify others belonging to the same category 