Actually, this has been a long debate whether it is mandatory to provide travels to/from country of origin and residence since it says on the form to only include "travels outside the country of origin and country of residence".
Regarding PCC from country of origin, according to my home country thread, it is still valid even if you get it before you leave. Well, they got their PPR without issues.
- are currently living there, or received the police certificate before leaving, the police certificate must be issued within six months before you apply.
- have lived there in the past, the police certificate must be issued after you last lived in that country or territory.
As I see it, the first clause applies to country of residence and origin, the second for previous residence.
For my case, I had my fingerprint from our embassy in my country of residence then authorized my brother to process the certificate in my home country.