A couple of things:
First, I don't think the tweet was "offensive," and I think it's unlikely people were actually offended. I do think the tweet was in bad taste and should be apologized for.
"Memorial Day means baseball and BBQ!" eh, that's not very good taste. I think it's FINE that people enjoy baseball and have barbecues on Memorial Day, but that's not what the day MEANS. The day exists because people have died so that we have the freedom to enjoy baseball and barbecue.
Second, I appreciate the apology from the White Sox: "We are sorry that one of our posts from earlier today made it seem as if we were insensitive to the true meaning of Memorial Day. That was not our intent, and we hope fans know how much we appreciate the sacrifices our veterans and service men and women have made to preserve our freedoms."
It's not a "we're sorry to anyone that was offended by our statement." It's recognizing that what was sent in the tweet was not a particularly good decision, owning the mistake, and clarifying what the intent was.
No one believes the White Sox are insensitive to the military or the memories of those who died. But it's also OK to say you are sorry when you know you have used bad judgment.