Chizuk Emunah (Pt 2) Under the Microscope: Chapter 28

Mark 2:25, 26, "And he [Jesus] said unto them, Have ye never read what David did when he had need and was an hungered, he and they that were with him? How when he went into the house of God, in the days of Abiathar, the high priest, and did eat the shewbread, which is not lawful to eat, but for the priests, and gave thereof to him that were with him." This passage is also to be found in Matthew 12:3-4, and in Luke 6:3-4; but all these authors have fallen into the same error, and labour under the same misconception. For this happened in the time of Ahimelech, the priest, and not in the time of Abiathar, as may be seen in 1 Samuel 21:1, "David came to Nob, to Ahimelech, the priest," etc. But Abiathar was one of the sons of Ahimelech, the son of Ahitub, who escaped and fled after David. Now, from the express question put to him, we see that David came alone to Ahimelech, and that no one was with him; "Why art thou alone, and no man with thee?" 

Finally, we get to Mark, considered the earliest and most theologically primitive of the four gospels. The scholarly consensus is that Mark was written before the other three gospels, and is therefore the most trusted by skeptical scholars.

Troki is referencing two passages in 1 Samuel and one in 1 Chronicles.

and Zadok the son of Ahitub and Ahimelech the son of Abiathar were priests, and Seraiah was secretary (2 Samuel 8:17)

Then David came to Nob to Ahimelech the priest. And Ahimelech came to meet David trembling and said to him, “Why are you alone, and no one with you?” (2 Samuel 21:1)

And the scribe Shemaiah, the son of Nethanel, a Levite, recorded them in the presence of the king and the princes and Zadok the priest and Ahimelech the son of Abiathar and the heads of the fathers' houses of the priests and of the Levites, one father's house being chosen for Eleazar and one chosen for Ithamar. (1 Chronicles 24:6)

Let's take a look at some background of Abiathar. He was:

"The son of Ahimelech the high priest. He was the tenth high priest, and the fourth in descent from Eli. When his father was slain with the priests of Nob, he escaped, and bearing with him the ephod, he joined David, who was then in the cave of Adullam (1 Samuel 22:20-23; 23:6). He remained with David, and became priest of the party of which he was the leader (1 Samuel 30:7). When David ascended the throne of Judah, Abiathar was appointed high priest (1 Chronicles 15:11; 1 Kings 2:26) and the "king's companion" (1 Chronicles 27:34)."

The International Standard Bible Encyclopedia mentions Troki's argument as well.

to get rid of the testimony of Jesus (Mark 2:26) to the effect that Abiathar was high priest and that the sanctuary at Nob was "the house of God," it is affirmed that either Jesus or the evangelist is here mistaken. The proof alleged for this is that Abiathar's service as priest did not begin till at least a few days later than the incident referred to. This is merely finical, though it is an argument that is sometimes used by some scholars.

So, Troki is griping over a minor detail. Abiathar was the high priest, yet his service did not begin until shortly after the incident with the showbread. Notice that Jesus, in this passage, says that it was in the days of Abiathar, the high priest. He did not say that it was in the days that Abiathar held the office of high priest. Yet, it was certainly in Abiathar's days. So this objection is simply pedantic.