The FPI says (at this point in the season) that given BYU's FPI rating and the rating's of their future opponents, BYU would be predicted to finish 9-3, which would leave them with zero probability of making the CFP.  I don't think any 9-3 team is going to make the CFP.

If BYU were 12-0, then the calculus changes, but this is not specifically addressed by the FPI (a "what if" perfect season).  The article makes a conjecture when it says, "Considering BYU's ranking in the CFP rankings throughout last season, even a 12-0 BYU might miss the CFP cut."  That is not based on the FPI, but is based on the author's personal perspective.

The probability that BYU has a perfect season is very low (as it is for all teams).  The probability that BYU has a perfect season and makes the CFP is low, but it is definitely greater than 0.0%.