Right. Having a "bizarre political background" is totally solid evidence of murder. 
Oswald is not "linked solid" to anything.
Oswald is not "linked solid" to anything.That's an assertion.
Having a "bizarre political background" is totally solid evidence of murder. 
Not that alone. However, it's probative circumstantial evidence when combined with:
-- Physical circumstantial evidence.
-- Behavioral circumstantial evidence.
You ignored the other evidence.
Staying "on topic":
Did Oswald smoke (cigarettes)?
--- Some smokers murder.
--- Some murderers smoke.
A nicotine habit is immaterial as to Oswald's guilt in two (2) murders: John F. Kennedy and JD Tippit.