It is supposed to be based on how your original ticket is booked, AFAIK.
That is, if your original ticket was booked with married segments, then the agent is most likely going to require business availability on all 3 segments in order to just change the middle segment to business.
If no married segments were involved originally, then it should be no problem for any agent to change you to business on the middle segment if availability opens up on just that segment.
The problem is that now, many agents are taking their married segment change "logic" to the extreme, and requiring availability on everything in order to make a change on one segment, even if married segments are not in play.
It's completely YMMV, and in any event worth a few HUCAs if you see availability open up on your middle segment.