Conjecture on regular holonomy and Lie structures on infinitesimal holonomy groups

Let $\cal F$ be a Riemannian foliation, let $H_p$ denote the holonomy group at $p$, and let $\mathcal V_p$ be the corresponding vertical space. The inclusion $H_p\subset \operatorname{Iso}(\mathcal V_p,\mathcal V_p)$ places $H_p$ inside the isometry group of $\mathcal V_p$. Regular-holonomy Lie-structure conjecture. The foliation has regular holonomy if and only if $H_p$ inherits a Lie structure from this inclusion. The conjecture concerns the relation between bounded holonomy, regularity of holonomy, and smoothness of the infinitesimal holonomy groups; the supplied text gives no resolution.