Incorrect rule interaction
When Blood Splatter Analysis enters the battlefield it does 3 damage to "target creature an opponent controls". Opponent targeted Venerated Rotpriest and no poison counter was given. Fynn, the Fangbearer was only other creature and no other cards were in play that would affect that interaction.
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Johnny Bartlett#16254
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Rezzahan#77802 commented
Because it is an ability that targets your Rotpriest, not a spell. The spell has no target.