Firstly, Luffy wasn't stronger than Doflamingo until he gained Future Sight.
Secondly, Big Mom sent Cracker to handle one half of the duo who beat Doflamingo, which is exactly how the news was spread. Re-read what Bege told his subordinates about what his "COMRADES" did post Dressrosa.
Besides why the bias in this instance alone?
I'm pretty sure you'd be mad if I used "Kaidou sent the Flying 6 to capture Yamato" to say she's Vet level.
Or if I said "Kaidou sent Jack to capture Luffy & Law in Act 1" to prove Jack > Kata.
Or if I use the fact that GreenCow was sent to capture Nika Luffy who beat Kaidou to prove GreenCow > Kaidou.