[panda-giddiness]

> Just because X implies Y does not mean ~Y implies ~X.

As others have mentioned, X implies Y does in fact require ~Y implies ~X. I think your example is confusing because "the government is corrupt" means many different things, but you're using it in a rather specific way ("the government is protecting SBF"). The equivalence of `X implies Y` and `~Y implies ~X` is more manifest through the following example

   "The government is protecting SBF, so SBF won't go to jail"

and

   "SBF went to jail, so the government wasn't protecting him."