(Spoilers Everything) Robert's Rebellion timeline and how it supports R+L=J

I was having this debate in another thread, but I thought it was worthy of it's own post. Some were arguing that the timeline does not allow for the R+L=J theory to be true because there were more than 9 months between Rhaegar leaving for King's landing and the events at the TOJ. However, according to the sources I found, that isn't true at all. I found this awesome tool:

https://app.plotist.com/timelines/562556dd50e3850300c5b353

According to this timeline, Rhaegar left from King's landing around the exact same time that Ned married Catelyn (and Robb was conceived at this same time). Now, if we look here: http://awoiaf.westeros.org/index.php/Robb_Stark

"Upon his return from the war, Catelyn greeted Ned with an infant Robb"

So, we can use that to deduce that a little more than 9 months passed between Rhaegar leaving for King's landing and Ned returning from war (give or take a month given that "infant" could mean a month, a week, or even a day old).

Now, from that we can say that if Jon was conceived shortly before Rhaeger left from King's Landing, the timeline actually fits perfectly.