Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type

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Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type ²G₂, and that if S is a Ree group of type ²F₄, then Γ is (up to point--line duality) the classical Ree--Tits generalised octagon.