Refocus is a poor man's Delay.
The start of a round is not much of a concept in DND. So, who cares if you go first in any given round? There are no effects that occur at or until the end or beginning of a round. With a circular initiative system (i.e. not rolling every single round), beginning and end of rounds in DND no longer matter.
For example:
If A delays, he can go:
BACDE or BCADE or BCDAE or BCDEA
If A refocuses and C has the first init (and assuming A beats C on the refocus), his only option is:
ACDEB
Delay does everything that Refocus does and more. Even if you roll init every round (or not). So, why have a silly Refocus rule?
PS. I have never heard of Defensive Refocus. When used with rerolling init every round, this is a silly rule too. You get to do more than just fight Total Defensive, you also tend to win init the next round. This totally blows away the Total Defensive rule when rerolling init every round like your DM does since nobody would ever take the Total Defensive action. They would always take the Defensive Refocus action. In fact, they would take the Defensive Refocus action instead of the Total Defensive action every time even if they did not reroll init every round. This sounds like a house rule and a bad one at that.