I'm not a lawyer but my thought process is that the "parallel construction" is going to include some chain of information/observation > probable cause > search > evidence and parallel construction is going to include dishonest testimony in the observation or probably cause area.

In reality I know that its difficult and unlikely to be proven or prosecuted, but it seems like that would be perjury.

Honest question though and I'm curious if someone with more expertise can explain where I'm wrong.