Listen to the line again:
For my dissertation, I was assigned the USS Kelvin.
He was not assigned to the USS Kelvin. He was assigned the topic of the USS Kelvin. His dissertation likely discussed the circumstances of its destruction and the leadership choices that were made during it.
This is reinforced later in the movie based on Kirk's line that Pike knew things about the Narada:
KIRK: Fact: the same anomaly -- a lighting storm in space -- that we saw today also occurred on the day of my birth, before a Romulan ship attacked the U.S.S. Kelvin. (to Pike) You know that, I read your dissertation. Which was good.
This is a not-uncommon choice for real-world History Ph.D. dissertations, for example "The British Air Campaign during the Battle of the Somme, April-November, 1916: A Pyrrhic Victory" (just to pick one battle dissertation I found quickly).
Dissertations are frequently hundreds of pages long (that one is 430) and require years of reading and studying logs and letters and interviewing co-workers and witnesses. I don't doubt at all that the author of a dissertation could acquire a sense of the personality of the central character in it.
An aside: The novelization by Alan Dean Foster is sadly no help in this case. For whatever reason, the reference to a dissertation isn't there:
"Captain Christopher Pike." Tilting his head slightly to one side, the Starfleet officer studied the bruised face of the much younger man. "I swear, I'm looking at you--and I'm staring right at him."
Kirk eyed the older man sharply. What the hell...?
In the course of the ensuing conversation Kirk realized he had absorbed more alcohol on his injuries than found its way to his stomach. Wary but riveted, he listened in silence to the visitor's delineation of a history he barely knew.
"Your father didn't believe in no-win scenarios," Pike finally concluded.
(Bold emphasis mine.)
Kirk's later reference to Pike's dissertation is still there and makes less sense since the first reference is gone, but it doesn't provide any more detail than the movie.