Batting Out Order or Just Wrong Numbers?

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... among the veteran umps that I was working with yesterday was that we would simply bring up the correct batter and she would assume the 1-0 count. All action by previous incorrect batters is now correct because of the pitch thrown to B5. I'll try to use the standard line-up format to explain this again.

Lineup for top of inning

B
C
D
E
F

D comes to bat instead of B, singles
C comes to bat, doubles - making D now legal, D goes to third
B comes to bat, takes a ball. Defense notifies that we have batting out of order.
E replaces B and assumes the 1-0 count.

Now, there was a great deal of discussion surrounding this scenario. I'm not confident that this is the correct solution, and would welcome other's input.

thanks,