Unfortunately there is no stats provided. Thus, if you are interested, you have to invest some time. I am 95% sure that you have started between 130 and 165 games of your 295 games.
What do you mean by starting player being "balanced"? The starting player is not balanced because it is determined randomly. What "balanced" distribution do you expect or wish?
I well believe that your opponents have started more games than you - because that is 50% likely. The probability that you started exactly the same number of games as your opponents is practically 0% (even if you had played 296 instead of 295 games). Your feeling seems to be that your opponents started way more games than you - which is most likely due to selective perception.
And again I add some constructive information at the end of my post - perhaps this is interesting to some readers...
The starting player in Backgammon has a 51.327% chance of winning. This probability is calculated by averaging out all the 15 starting rolls and assumes equal skill of the players.
If the starting player rolls a 3-1 (best starting roll), he has a 55.51% winning chance.
If the starting player rolls a 4-1 (worst starting roll), he has a 49.65% winning chance.
Only with 4-1 starting is a disadvantage. All the other 14 starting rolls give an advantage to the first player.