Essentially the point is that you can't get a refund on the monies paid for a (non-refundable) fare. So any fare replacing the previous fare must cost at least as much as the previous fare, otherwise you will have paid more than you will be charged and you will be entitled to a refund of money. To avoid this, BA is saying that you must have a new fare charging you at least as much money as you have already given them.
The "must comply with all provisions" would include things like minimum stay, sales restrictions, etc.
I'm not sure if the airline can simply make up a higher number for your ticket or if it's more complex; i.e. I don't know how to fix this if you can't find an appropriate fare. I only know how it occurs.