In a note of Freedman and Zuddas, they show that this is true for dimensions $\geq 4$.

In the "Background" section of the paper, they describe the solution in the higher dimensional case using surgery theory, but without any references.

Then they proceed to describe the 4-dimensional case. Here they use the fact that the complement of a point in a 4-manifold is smoothable. Hence one can describe a triangulation of a finite part of the complement of a point, together with a certificate of a 3-sphere tamely embedded.

It's frustrating that they don't give any references for the higher-dimensional case, but since you're in Santa Barbara, you could probably saunter over to Station Q to get the details from Mike once campus opens again.

In a note of Freedman and Zuddas, they show that this is true for dimensions $\geq 4$.

In the "Background" section of the paper, they describe the solution in the higher dimensional case using surgery theory, but without any references.

Then they proceed to describe the 4-dimensional case. Here they use the fact that the complement of a point in a 4-manifold is smoothable. Hence one can describe a triangulation of a finite part of the complement of a point, together with a certificate of a 3-sphere tamely embedded.

It's frustrating that they don't give any references for the higher-dimensional case.