evam īśvare paroktam eva anumānaṃ nirastam, na tv īśvaro ‘pi.

In this way I have refuted the inference to the existence of the Lord said by other scholars, but I have not refuted the Lord Himself. (NV, tarkapāda, end of sambandhākṣepaparihāra)

Thus, it is quite clear that:

• Bhavanātha (and perhaps also other Mīmāṃsā authors?) did not understand Kumārila’s refutation of theism as a refutation of any form of theism.
• This distinction might have looked obvious enough to Bhavanātha, since he did not feel the need to elaborate about that.