Krishna saved Draupadi. First of all, just so people know what we're talking about, here is the description of Krishna saving Draupadi form being disrobed in this chapter of the Sabha Parva of the Mahabharata:
When the attire of Draupadi was being thus dragged, the thought of Hari, (And she herself cried aloud, saying), 'O Govinda, O thou who dwellest in Dwaraka, O Krishna, O thou who art fond of cow-herdesses (of Vrindavana). O Kesava, seest thou not that the Kauravas are humiliating me. O Lord, O husband of Lakshmi, O Lord of Vraja (Vrindavana), O destroyer of all afflictions, O Janarddana, rescue me who am sinking in the Kaurava Ocean. O Krishna, O Krishna, O thou great yogin, thou soul of the universe, Thou creator of all things, O Govinda, save me who am distressed,--who am losing my senses in the midst of the Kurus.' Thus did that afflicted lady resplendent still in her beauty, O king covering her face cried aloud, thinking of Krishna, of Hari, of the lord of the three worlds. Hearing the words of Draupadi, Krishna was deeply moved. And leaving his seat, the benevolent one from compassion, arrived there on foot. And while Yajnaseni was crying aloud to Krishna, also called Vishnu and Hari and Nara for protection, the illustrious Dharma, remaining unseen, covered her with excellent clothes of many hues. And, O monarch as the attire of Draupadi was being dragged, after one was taken off, another of the same kind, appeared covering her. And thus did it continue till many clothes were seen. And, O exalted on, owing to the protection of Dharma, hundreds upon hundreds of robes of many hues came off Draupadi's person. And there arose then a deep uproar of many many voices. And the kings present in that assembly beholding that most extraordinary of all sights in the world, began to applaud Draupadi and censure the son of Dhritarashtra.
Second of all, Draupadi recalls the incident in this chapter of the Udyoga Parva of the Mahabharata.
O Kesava, the sons of Pandu, the Panchalas, and the Vrishnis being all alive, exposed to the gaze of the assembly I was treated as a slave by those sinful wretches. And when the Pandavas beholding it all sat silent without giving way to wrath, in my heart I called upon thee. O Govinda, saying,--Save me, O save me!
On top of that, Kunti mentions the incident in this chapter of the Srimad Bhagavatam:
My dear Kṛṣṇa, Your Lordship has protected us from a poisoned cake, from a great fire, from cannibals, from the vicious assembly, from sufferings during our exile in the forest and from the battle where great generals fought. And now You have saved us from the weapon of Aśvatthāmā. I wish that all those calamities would happen again and again so that we could see You again and again, for seeing You means that we will no longer see repeated births and deaths.
Finally, Madhvacharya describes the incident in this chapter of his Mahabharata Tatparya Nirnaya, one of the oldest commentaries on the Mahabharata:
When dushyAsana started disrobing her, draupadi started to remember kRushNa in a very special manner. At that time, another saree which was divine, very delicate and glowing like gold appeared on her body. As and when dushyAsana started snatching the sarees, a new saree appeared. Sinful dushyAsana could never reach the end. He was exhausted and sunk down in the assembly hall. When the pile of sarees started to grow like mountain, ignorant duryOdhana who was furious said “why are you delaying, take her to our house”.
So I don't think there's any reason to doubt the story.