Models for which Measurable implies Universally Baire?

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To begin, Universally Baire sets are Lebesgue measurable (slide 4 of http://www.ub.edu/RSTR2018/slides/Woodin.pdf). I was wondering if there are any natural models of ZFC where the converse holds, and sets are Universally Baire iff they're Lebesgue measurable. (It can't be ZF set theory because I am fairly sure that models such as the Solovay Model have all sets having both properties, due to determinacy)