Something that is true and factual, by definition, is true and factual regardless of what you, or I, or anyone believes or disbelieves. Who would it then be that determines that the "something" is true and factual?
Nobody can choose something to be objectively true or false. If this were to be true, who can make such a choice?
Does 'Allah' exist because millions of Muslims 'choose' to believe in the existence of Allah? Why not? Where would Allah exist - in what realm - determined by whom?
Truths are demonstrable and testable, faith is neither.
As usual, you quote that trite mantra. But, your quote answers none of the above questions. Are you avoiding the realities? Maybe DBT would like to answer the questions about his statements?
