PAF automatically keeps track of the "Last Date Changed" and it can be a useful search criterion in an Advanced Focus Filter. On the Edit Individual screen, you will see this date for each individual. The log is just a convenient list that is external to the database itself. As you have discovered, deleting or flushing the log doesn't change the database.
"Last Date Changed" can be seen in a gedcom file in this format: 1 CHAN 2 DATE 12 Oct 2006 3 TIME 21:25:40 Gedcoms created by FTM probably include the same information, so I don't think the information itself is the problem.
PAF is doing what it is designed to do. I suppose the question is "Why does FTM print the last date changed, if you haven't asked it to do so?" I think the solution will have to be found within FTM. Fortunately, FTM has its own support system, including a forum on GenForum. http://genforum.genealogy.com/online/http://genforum.genealogy.com/online/