Depends. Saying "thing X should not fail" is factually incorrect, when you called because thing X failed.

However I would not expect an airline customer support to make up a completely fictional flight that has never existed. Maybe they could confuse flights or read a number wrong, but making one up?

Humans won't fabricate too much but when confronted with yes/no questions and they have a 50-50 shot of being right and any blowback will likely be on someone else....they'll answer whatever to get you out of their hair.

Case in point, I asked my bank if they had any FX conversion fees or markup. Guy said no. I asked if there was any markup on the spread. Said no. Guess what? They absolutely mark up that spread. Their exchange rates are terrible. Just because there isn't a line-item with a fee listed doesn't mean there isn't a hidden fee in there. He's either incompetent or a liar.