Oh maybe..how about the depressed microphone for several minutes just right when the motorcade was passing through Dealey Plaza and then headed to the hospital. One of the umptyfive hundred coincidences just in the space of an half hour 
The biggest problem for the believers in a 1.14 / 1.15 shooting of Tippit are the combined timelines of Markham and Bowley. Their "estimates" don't have to be "spot on". There are two anchors which IMO make it nearly impossible to challenge these timelines, even when you give or take a minute or so.
First of all, we know that Markham arrived at the scene, at least two or three minutes (my estimate), prior to Bowley. Markham saw the shooting taking place and Bowley arrived shortly after it happened.
Secondly, we know that Bowley said he picked up his daughter from school at "about 12.55" and school bells tend to ring on time.
So, if you want to push back Markham's time, you also have to push back Bowley's timeline with the same amount of time, otherwise there is no way that Bowley could have arrived after Markham saw the shooting.
Markham said she left home at "a little after one" and that it could have been as late as 1.06 or 1.07. The walking distance from 9th street to 10th/Patton is one block which takes about 2 minutes, which would have her arrive at 10th/Patton at
the latest at 1.09.
The route Bowley described from the school to 10th/Patton takes an estimated 13 minutes, so if he picked up his daughter at "about 12.55" and allow a bit more time for traffic, he could and would have arrived at 10th/Patton
at roughly 1.10.Inbetween those to arrival times Tippit must have been shot.
So, what happens if you try to push back Markham's arrival time to (let's say) 1.14? It would mean that Bowley's timeline would have to be pushed back by 5 minutes also, but how does that work when you know he picked up his daughter from school at 12.55? Five minutes late would have left his daughter waiting for him for 5 minutes after school was out.... so, what's the reasoning there? Bowley got to the school 5 minutes late and somehow didn't notice it?
And what about Markham, where was she during those extra 5 minutes? Did she perhaps go for coffee halfway down the 2 minute walk it would have taken to get her from 9th to 10th street?