That's the thing, they don't. There's no source documentation links on snopes, politifact never does either, and Church Militant or Lifesite are downright frustrating in how their links just link back to other stories written by themselves.
I am unfamiliar with Church Militant and Lifesite, let's address the other two.
Snopes
At the end of each Snopes article is an infromation box, including name fo the fact checker, date published, date last updated, and a black button marked Sources. Clicking that will list all of the original sources.
To pick a non-political one, there was an article about Pins and Needles in Halloween candy.
https://www.snopes.com/fact-ch...
Clicking the sources button brings up:
The Associated Press. âoeMan Charged with Putting Needles in Halloween Candy.â
Minneapolis Star Tribune. 2 November 2000.
Gardner, Bill. âoeMan Arrested After Kids Get Tainted Candy.â
Pioneer Press. 1 November 2000.
Santino, Jack. Halloween and Other Festivals of Death and Life.
Knoxville, TN: University of Tennessee Press, 1994 ISBN 0-87049-813-4.
All of their articles list this. Many of the others with more specific information go to various governmental sites directly, this one is a bit of a soft topic in that public documentation is mostly available in the news, as health care reports are personal.
Politifact
Politifact it's hard to find a non-political example, so I apologize for picking one that you may have strong feeling about. It was about "Bloggers poison truth in claim about flu shot dangers".
https://www.politifact.com/fac...
Politifact embeds it's links within the article. This article contains the following links:
A link to the claim.
A link to the CDC website about children's flu deaths being 80% un-vaccinated last flu season.
Two links to the FDA about Thimerosal.
Two links about how vehicular antifreeze is not in flu vaccine.
A link to the FDA how Phenol is not in flu vaccines.
A link to the CDC about eg proteins for those with egg allergies.
Three links about formaldehyde, two to the CDC and one to the FDA.
If you look, those are original sources.
Conclusion
Snopes and Politifact both show all of their original sources so that you can double check their findings yourself. This doesn't mean what they post is 100% correct - merely that they provide the information so you can check yourself and that does greatly reduce speculative information and helps provide a check for mis-understandings of the source information.