Civil War could happen without Spider-Man and The Fantastic Four but it would require Marvel Studios to add some more heroes at a faster clip to their universe and it would require their movies not to be shiny happy feel good action films (and yes that is what all of the Marvel movies are even the great Winter Soldier despite everyone erroneously buying into that "Its a spy thriller" bullshyt). Civil War would require the MCU becoming a dark, morally grey, overly violent place. And considering Marvel built its billion dollar movie empire not going down that route I would say the odds Disney allowed them to go dark are slim and none.