This part is considered interpolation.
As per Kisari Mohan Ganguli's translation, Karna did not fail in Draupadi swayamvar as stopped by Draupadi in between. Although he didn't shoot the arrow but people present there including Pandavas regarded the mark as already shot. Karna strung the bow and was about to release the arrow but Draupadi denied marrying him:
And beholding the plight of those monarchs, Karna that foremost of all wielders of the bow went to where the bow was, and quickly raising it strung it and placed the arrows on the string. And beholding the son of Surya--Karna of the Suta tribe--like unto fire, or Soma, or Surya himself, resolved to shoot the mark, those foremost of bowmen--the sons of Pandu--regarded the mark as already shot and brought down upon the ground. But seeing Karna, Draupadi loudly said, 'I will not select a Suta for my lord.' Then Karna, laughing in vexation and casting glance at the Sun, threw aside the bow already drawn to a circle. ~Mahabharata: Adi Parva: Swayamvara Parva
These shlokas are present in Gitapress version with some note:
The note is in Hindi which says that these shlokas are not in other script and in the same chapter and next chapter it's stated that Karna couldn't string the bow:
Then those princes--Karna, Duryodhana, Salwa, Salya, Aswatthaman, Kratha, Sunitha, Vakra, the ruler of Kalinga and Banga, Pandya, Paundra, the ruler of Videha, the chief of the Yavanas, and many other sons and grandsons of kings,--sovereigns of territories with eyes like lotus-petals,--one after another began to exhibit prowess for (winning) that maiden of unrivalled beauty. Adorned with crowns, garlands, bracelets, and other ornaments, endued with mighty arms, possessed of prowess and vigour and bursting with strength and energy, those princes could not, even in imagination, string that bow of extraordinary stiffness. ~Mahabharata: Adi Parva: Swayamvara Parva
Now, this Karna (the word Karna is used in Sanskrit Shloka) can be Dhritrastra's son Yuvutsu also. So, can't be considered as valid point. But in next chapter, it's again stated that:
And that bow which Rukma, Sunitha, Vakra, Radha's son, Duryodhana, Salya, and many other kings accomplished in the science and practice of arms, could not even with great exertion, string, Arjuna, the son of Indra, that foremost of all persons endued with energy and like unto the younger brother of Indra (Vishnu) in might, strung in the twinkling of an eye. ~Mahabharata: Adi Parva: Swayamvara Parva
Here, the word Radheya is used in shloka which raises high probability that earlier shloka (which says Karna was able to sting the bow) is interpolated.
And if she denied, how moral/right was it? What was the reason her denying it?
As there are 2 different version of story: one in which Draupadi denies and another where Karna fails. If version 2 is true then this question is not valid. If version 1 is true then, it's answer is not clear form Swayamvara Parva but the next chapters mention that Draupadi had been appointed wife of Pandvas in her previous birth itself as discussed here.