Since the 1500s, 'pat' has meant correctly/precisely/exactly to the purpose etc. One of the earliest uses, for example, was an author writing of his surprise that his doctor had described his disease "so pat".
Today, we use it in exactly the same way when we say proudly of our children/grandchildren that they "got their lines down...(or off, as Jabba says)...pat during the school play."
I'm not sure where your husband got the 'packed' idea other than just mishearing it for 'pat'.