From Wall's Surgery on Compact Manifolds, P9:
Observe that $S^r \times D^{m−r}$ is parallelisable.
If $m > r$, this is true, because spheres can be embedded in Euclidean space of one dimension higher, so $S^r \times D^{\ge1}$ immerses into Euclidean space of the same dimension. Then the pullback of the (trivial) tangent bundle of Euclidean space gives a trivial tangent bundle of $S^r \times D^{\ge1}$.
But what if $m = r$? Then let $r = 2$ as an example, we get $S^2 \times D^0 = S^2$, which is not parallelizable.
Is Wall's statement wrong, or am I misunderstanding something about tangent bundles?