Tubular rivets are much stronger than double-cap rivets. Since the Naito is a sling bag, the strap pulls away from the bag at the attachment point, which makes double-cap rivets unreliable, since they can pop apart when pulled with opposing force.
On the other hand, tubular rivets are made to withstand this force and will stay in place (especially when reinforced with leather on the backside of the fabric). So, in a nutshell, the Naito is designed to stand the test of time!
Please don't substitute double-cap rivets for the tubular ones when making the Naito. Also note: tubular rivets need to be set with a Tubular Rivet Peening Tool and a non-rubber mallet.