I think you're fine...really.
Think of it this way:
If you were born on 01/01/01, you would have your first birthday on 01/01/02, NOT 01/02/02.
You would be one year old ONE YEAR AFTER YOU WERE BORN, not one year + 1 day. Most people celebrate their birth on the EXACT DATE that they were born, right?
However, if you began living with your Common-law partner on February 29th in a leap year, you would use March 1st of the following year as your official date...I think?!?!
You are not common-law until you have been living together, and fighting over the remote control for ONE YEAR (or more in some provinces) , but...I like your `story'.