Examine that with logic
Kobayashi officially stated that Nero is teh same age as Dante was in DMC3; this is 19. He also said that DMC4 is ten year after DMC3. that puts Dante(and thus Vergil) at 29 in DMC4. That means vergil was 10 when nero was born, and 9 when Nero was concieved.
Ergo, Nero is NOT Vergil's son. Nero has more call backs to what we know of Sparda himself(red, blue and purple clothing, willing to do all for the woman he loves, rebelling against the "higher order", Yamato glows purple in his hands...the fact he could HEAL Yamato) than just Vergil. Plus with 2000 years from when Sparda rebelled on Hell, he likely had fallen in love with a few human women between then and Eva, meaning he left other bloodlines, Dante and Vergil are just the only children of his known to be alive in the current era.
And then there's the idea that Nero is infact Sparda himself reincarnated after his death. The projected time between Sparda's death and Nero's birth make this a likely option for Nero's origins. After all. Berial was referring to SPARDA with that line, not Vergil, since teh last time Berial was out was during Sparda's rebellion.