They can but it looks bad on them. If the packet is reconstructed the date should be the date of the offense (the date it actually took place) and then the signing date should be the date you actually sign it. It cannot be back dated to the original signature date.
If you were late for work on the 3rd of Oct 2012. and they rewrite the counseling statement it should state on 3 Oct 2012 you were late for work. Then it should have today’s date on it for your signature.
Course(s) of Action to Consider
You may want to consider disagreeing with the counseling statement and then putting an explanation in the block something like. I have no way to verify the information contained in this counseling session with regard to the alleged incident, the time/date and circumstances cannot accurately be recalled because this counseling is a “Reconstruction.”