- dizzystar would enjoy working remote
- it would be hard for dizzystar to find other remote-working opportunities
- hence, dizzystar would be willing to work for a discounted rate, in order to be remote
In their perspective, there is no "right or wrong". It's purely a matter of negotiation leverage. You have a couple options here:
- admit they are right, and accept a discounted rate
- claim that your rates are final and not negotiable
- claim that you don't value remote working, but because you value them as a client, you're willing to negotiate on your rate
Option 2 is more likely to get you a higher rate, but also more likely to drive them away. Option 3 involves accepting some discount, but at least you minimise the leverage they think they have over you.
This discussion over semantics is not helping anyone. Just treat it as a negotiation game, and play it the way you would any other negotiation scenario.