Yes, it was actually Samuel who came. The text notes this without any further comment to the contrary.
The king said to her, “Have no fear; what do you see?” The woman said to Saul, “I see a divine being coming up out of the ground.” He said to her, “What is his appearance?” She said, “An old man is coming up; he is wrapped in a robe.” So Saul knew that it was Samuel, and he bowed with his face to the ground, and did obeisance. (1 Samuel 28:13-14 NRSV)
Seeking the dead, though prohibited by Deuteronomy 18:11, existed in Israel as late as the time of Isaiah, who condemned it (8:19-20). Though some places in the Bible describe the dead as knowing nothing (Ecclesiastes 9:5), other texts do depict the spirits of the dead (רְפָאִים) as speaking (Isaiah 14:9-10).
Although a false spirit isn't foreign to the Bible (see 1 Kings 22:19-23 for a false spirit of prophecy), there is no reason to think that the spirit of Samuel in this text is a false spirit. Samuel responds to Saul in death similarly to how he responded while alive.
This is what Samuel said to Saul while he was still alive, after the battle against Amalek:
Samuel said to Saul, “I will not return with you; for you have rejected the word of the Lord, and the Lord has rejected you from being king over Israel.” As Samuel turned to go away, Saul caught hold of the hem of his robe, and it tore. And Samuel said to him, “The Lord has torn the kingdom of Israel from you this very day, and has given it to a neighbor of yours, who is better than you. (1 Samuel 15:26-28)
When brought up from the dead, the spirit of Samuel speaks in the same manner, even using the same phrase at one point. Compare the bolded parts to the bolded parts in the previous section:
Samuel said, “Why then do you ask me, since the Lord has turned from you and become your enemy? The Lord has done to you just as he spoke by me; for the Lord has torn the kingdom out of your hand, and given it to your neighbor, David. Because you did not obey the voice of the Lord, and did not carry out his fierce wrath against Amalek, therefore the Lord has done this thing to you today. (1 Samuel 28:16-18)
Finally, Samuel's spirit predicts Saul's demise the next day at the hand of the Philistines.
Moreover the Lord will give Israel along with you into the hands of the Philistines; and tomorrow you and your sons shall be with me; the Lord will also give the army of Israel into the hands of the Philistines. (1 Samuel 28:19)
This is exactly what happened (1 Samuel 31:6).
This is also the interpretation assumed by all ancient post-biblical sources of which I am aware (Josephus, Antiquities 6.14.2; Leviticus Rabba 26:7; Midrash Shemuel 24).