The ball correctly identifies the score of the game on July 13, 1950 despite the date of July 14, 1950 on the ball itself. Why? I haven't a clue.
In the game on the thirteenth Robinson appears to have played the whole game and was credited with 3 putouts and 4 assists. He also as the second baseman would have participated in throwing the ball around the infield after infield outs, which would have allowed him to touch more game balls than those he fielded.
On the other hand a new ball entering the game conceivably could have been fouled off into the seats during the first at bat for that ball in which case Robinson would not have touched it. The ball looks like it received a bit of a beating, but when that occurred (during the game or after) is unknown.
In the game on the 14th of July, which Brooklyn won 1-0, Robinson also played the full game, but did not record any chances in the field. He still would have been a participant in tossing the ball around the horn after after infield outs though and also receiving throws from right and center field.
Another question, since the game score and date do not match, is why don't they match. The writing on the ball could have been done by the original recipient. Perhaps he caught a foul ball at Wrigley on the 13 th and wrote on the ball the next day looking at a calendar. Who knows? One would think that if the ball was entirely bogus, which I doubt, that whoever wrote on the ball later, with an intent to deceive, would not have made such an error. I see no advantage in terms of ball value to memoralizing either of the games in question with such an inscription, correctly or incorrectly.
Finally I wonder if forensic analysis using DNA testing has ever been used to determine who has touched which (or whose) balls. Also could DNA testing be used as an adjunct in autograph authentication?
Several years ago I had the opportunity to photograph a dual signed ball by Ruth and Gehrig. I confess to handling the ball without white gloves. On that ball I suspect that my DNA is there on the leather with the DNA of both Babe and Lou.
Given the arguments presented above one cannot say for sure, but it would seem more likely than not that Jackie touched your ball, if in fact that ball was in Chicago during July of 1950.