If an individual is the owner, but not the beneficiary of a small annuity, is the total prinicple considered their asset?

Actually your responses while helpful misconstrue part of the question. The $1500 per year is dispersed to the individual owner, but the death beneficiary of the principle is not the owner. Nonetheless, your main point is the same as I suspected: that the "owner" of the policy is in fact the carry of the asset and therefore the entire annuity counts as part of their financial holding for purposes of Medicaid eligibility.

The owner is the owner, because they have control of it and could go so far as to send it to a charity, to themselves, or anyplace they choose. So if Grandma owns an annuity that is benefiting someone else, Medicaid will frown on that and expect Grandma to use it to pay for her own NH bills. That $1500 per year is a "gift" to the beneficiary. The principal is Grandma's asset.