You are (ignorantly or purposefully) ignoring the fact the apostle was identifying himself with the believing community.
It is the same with the Passover story. it is not when THEY came out of Egypt; rather it is when WE came out of Egypt. Part of the community regardless of what century it is or who was actually alive at the time.
Yes, a perfectly understood acceptance of identifying with a given group.
A modern day example would be if you were talking to someone about a specific sports game and they asked you "Who won"?, and you would reply WE won.... meaning the team you supported. No one would think you had actually played in the game.
or if you are talking with folks from another church about missionaries you might say "We will be having a group to go to wherever on mission work in whatever time span, even though you may not be alive when that happens. You are part of the church who will have that experience, therefore it is appropriate.