One thing to remember is that though the alternate timelines share the "Always a man, always a lighthouse, always a city" causality, they are not really directly comparable as the timelines can be so different depending on choices which go back decades.
The most compelling piece of evidence for a direct link between Bioshock 1 and Infinite or between Booker and someone in the Rapture timeline, if it is that and not a mistake by 2K, is the fact that Booker is able to use the Bathysphere in Rapture when we are told in Bioshock that only Andrew Ryan and his close relatives can use it, pointing towards Booker being either Ryan himself or a relative. This could either be a mistake OR they could be in Rapture before this rule was enforced. Alternatively it could just be Elizabeth weaving elaborate plot-fu.
However saying that Booker is Ryan/Relative is a bit inaccurate as Ryan isn't Booker, they are completely different men. Much like Booker is different to Comstock, they are the results of entirely different series' of events, though Booker/Comstock are much more closely linked (and also a special case imo).
In actuality I DO think that the relation IS between Booker and Jack. Let me explain.
The reason I think this is because the most reasonable link between timelines is that "A man" in each timeline is simply a role filled by an appropriate actor, the Booker/Comstock relation is special case as it involves people DIRECTLY meddling with the multiple timelines. This allows Booker to player the "A Man" role in two timelines simultaneously. Depending on the choices which are made in the past, in some timelines Booker will NEVER EXIST/HAVE EXISTED AT ALL.
tl:dr
The Booker/Comstock relation is special because it involves direct timeline tomfoolery by the Luteces who mix together two of Bookers timelines, i.e NOT NATURAL.
"A Man" is simply a role filled by an appropriate "Actor" in each Timeline, it is not always the same man, if ever.
The same goes for "A City", there just has to be one, who builds it or visits it via the Lighthouse is variable and depends on the Timeline.
In Bioshock 1, Jack is "A Man", Rapture is "A City". In Infinite, Booker plays the role of "A Man" in two timelines.
Personally I think this is the most "logical", or rather least outlandish explanation.
One interesting thing to consider, technically, the only character to "die" in Infinite is Elizabeth. Once the timeline is resolves, she will never get the opportunity to grow up into the woman we see in the game, Anna grows up with Booker (presumably) and Elizabeth never gets to exist.
