The double fishermans knots as backups would greatly add to the security of the square knot. I would say those would make it as secure as it would ever need to be. Without backup knots of some kind - whether they be double fishermans or simple overhand knots - the square knot is NOT secure.

But theses backup knots would NOT add to the STRENGH of the square knot one bit. Your climber person here has come up with a secure knot, I'll give him that. But why would he use a knot that is less strong than others (like just using a double fishermans as the bend in the first place)? With modern ropes, sure, having a square knot eat up half of the ropes original strength is adequate for rapelling. But why would one go to the trouble of tying a square knot, and then two double fishermans knots as backups when they could have just tied one double fishermans in the first place and come out with a stronger knot that is just as secure as the odd square knot contraption?

I'm not sure how you'd tie a double fishermans as a backup knot anyway, since you need both running ends of the ropes to tie this knot. The climber guy probably meant a double overhand knot rather than a double fishermans.