  In this paper, we first prove that any closed simply connected 4-manifold
that admits a decomposition into two disk bundles of rank greater than 1 is
diffeomorphic to one of the standard elliptic 4-manifolds: $\mathbb{S}^4$,
$\mathbb{CP}^2$, $\mathbb{S}^2\times\mathbb{S}^2$, or $\mathbb{CP}^2\#\pm
\mathbb{CP}^2$. As an application we prove that any closed simply connected
4-manifold admitting a nontrivial singular Riemannian foliation is
diffeomorphic to a connected sum of copies of standard $\mathbb{S}^4$,
$\pm\mathbb{CP}^2$ and $\mathbb{S}^2\times\mathbb{S}^2$. A classification of
singular Riemannian foliations of codimension 1 on all closed simply connected
4-manifolds is obtained as a byproduct. In particular, there are exactly 3
non-homogeneous singular Riemannian foliations of codimension 1, complementing
the list of cohomogeneity one 4-manifolds.
