Name or theory for a particular phenomenon pertaining to ideological possession Is there a name or a theory for when someone alters a truth to strengthen their point(delusion)? 

For instance, remember when President Trump carried out his plan to deport "illegal" immigrants and the lefties painted a different picture by their "Day without immigrant" story to portray the administrators as cold mean bullies, as opposed to saying "Day without ILLEGAL immigrants"? 

It is a phenomenon where individuals will consciously alter something, not intentionally to lie malevolently, but strengthen their (obviously) weak point(something to do with ideological possession).

Is there an official name or theory for this, like, "So-and-so's theory of  such and such" or is there rather a study with conclusive data/research on the phenomenon?
There is a fallacy in thinking called "confirmation bias" in which one only looks at or perceives "facts" in light of, or to support, their pre-conceived notions.
Here is the definition of confirmation bias:


  The tendency to interpret new evidence as confirmation of one's existing beliefs or theories.


See confirmation bias definition.
Of interest see also article in Psychology Today