Line-Up Card Problem

[Baseball_North]

Here is the situation....

In my game last night, I go in to pinch hit for the ninth hitter in our order. It is the bottom of the 7th inning. 2 outs.

I chop a crappy hit that bounces off the plate, and I manage to beat it out at 1B for an infield single. The coach of the other team then calls time and goes to the umpire. No one knew what the problem was. After a discussion between the umpire and the visiting coach, the PU said that we batted out of order and that there were 3 outs.

There was confusion, but the defense left the field, and my team took the field for the top of the 8th. While out team was warming up in the field, I just passed by the umpires (I know them, have umpired with them on numerous occasions), and asked them what the problem was.

It turned out that our eighth and ninth batters were incorrectly placed on the official line-up card. Their names were in the right order, but my coach accidently flipped their numbers. So I was talking to the umpires, and I told them, "shouldn't we just be going by the name on the line-up card". Then my coach came over and started talking, and the PU said that we were right, and the name on the card is what matters, and told my team to get back up to bat to finish the bottom of the 7th inning.

So my question is.... what actually has more power with respect to line-up screw-ups? Do you go by the name or by the number?

Also, wouldn't it be too late for them to complain, if I pinch-hit and completed by at bat?