# Ambient Isotopy

From Hirsch's Differential Topology, p. 180.

The first of the isotopy extension theorems says;

Let $A\subset M$ be a compact submanifold and $F:V\times I \rightarrow S^{3}$ an isotopy of $A$. If either $F(V\times I) \subset \delta M$ or $F(V\times I) \subset M - \delta M$, then $F$ extends to a diffeotopy of $M$ having compact support.

What I don't understand is why this does not imply that every isotopy of knots is automatically an ambient isotopy. Since knots are compact and $S^{3}$ has no boundary.