One swami from Himalayas told an interesting story:

A man suddenly became blind due to some strange disease. He goes to many doctors and tries all sorts of medicines. He is even operated upon yet he remained as blind as before. Every means he tries became invalid. He gets frustrated and becames vexed with all the promises of the doctors. At last he is taken to one famous surgeon, who says that he could help him get sight. After much coaxing the blind man agrees to the operation.

After the operation, the doctor comes to the patient saying: ‘Congratulations - the operation went successful and now I will open your bandage’. The surgeon removes all the coverings and asks the patient to open his eyes.

The blind man says he would not open his eyes unless the doctor promised that the operation had really been successful and would guarantee that his eyesight has been restored, since in the past he had been so disappointed by the promises of so many doctors. The surgeon says that all indications were that the operation had been successful but that he could not know for certain until the patient opened his eyes and discovered that he could see.

Still, the blind man refused to open his eyes unless the doctor assured him that this particular operation had been fully successful. Now the doctor could not provide any further proof other than telling the stories of how successful other similar patients had been and assuring the blind man that there was no reason to doubt that this operation had also been successful. But the real success of the operation could only be established by the patient opening the eyes and testing whether he can see or not.

Evidence of Vedanta is exactly like that. It provides a means to know but the knowledge has to be gained by the seeker through his self-effort. Hence it tells us that one has to do manana (reflection) and nididhyasana (meditation) after hearing (shravana) the facts from the Guru.