I think technically you may be correct, but without testing it I can't say for certain. Assuming you are correct, in reality that is still the last accessed date. You can't tell it that you want to know the last access date, but only when it is by a user and not the system. Without tools that would cost additional money, the only way I can think to do something like this is to enable security auditing for process start/stop and then deal with the log entries that are created as it should associate users to it. That is at least something you can tell Lansweeper to pull in. It may be overwhelming, but it is something you can filter against.
EventID is 4688 and it shows up in the security log.
secpol.msc
Local Policies\Audit Policy\Audit Process tracking