It has been confirmed by Jeremy Crawford that Cutting Words can cancel out an enemy's critical. As Dale M explained in his answer to the issue, Cutting Words does not apply a modifier to the roll. Instead, it changes the base roll itself. He lists the full quote, but let me just emphasise the particular wording:
...substracting the number rolled from the creature's roll.
Now, Barding Inspiration has this rule (PHB page 33, emphasis mine):
...you use a bonus action on your turn to choose one creature other than yourself within 60 feet of you who can hear you. That creature gains one Bardic Inspiration die, a d6. [...] the creature can roll the die and add the number rolled to one ability check, attack roll, or saving throw it makes.
The two rules are very much alike, with the only difference being that one buffs up your rolls while the other one weakens the rolls of your enemies. Therefore, if one can cancel a critical, can't the other give you one?
If I roll an 18 and get a 2 or more on my Bardic Inspiration die, do I get a critical hit?