Depending on how you approach this there are two reasons, the first approach was I was answering the question in this thread of do you ignore Getty's letter or do you send one letter, so my response was based on the premise that you're going to send one letter and be done so you must cover all of your steps in one letter.
I myself did not send my offer with my first letter as my approach is more of I am going to make this a serious time suck as well as being a thorn in Getty side approach. However, at some point I did make what I considered to be a reasonable offer contingent on proof of claim. The reason for the contingency is that Getty is still sending me an invoice but has not yet proved that I owe the money.
As to what a judge would do or not do you can never tell but I believe it shows good faith on the part of the letter recipient when you can say that (in my case):
1) I dispute this claim and any infringement however, if there was infringement it was innocent and nonwillful and I have proof in the means of screen captures of where the image was obtained showing the image belonging to someone else and being offered up for free. Also Getty is currently being sued by Rock Photo for infringement in Getty's defense is that the infringement if at all was innocent and therefore they should not have to pay.
2) I have requested that Getty provide me proof of their claim of exclusive rights to the image in question as well as the signed contract giving them rights to pursue and collect damages.
3) I have let Getty images know I am willing to continue to discuss and negotiate this claim.
4) in the response letters to complaints filed with various agencies Getty always claims they cannot provide proof because of confidentiality agreement signed with the artists. I have offered to sign a similar agreement binding me not to discuss, disclose or reveal anything in the proof I have requested except for the purpose of settling this claim to which Getty has replied they still will not provide proof as it just takes too much time and expense.
5) I made Getty images what I considered to be a reasonable offer contingent on proof.
Items three through five are all contingent upon proof being provided. Since you never know how a judge will react or respond I think it is best to cover all of your bases as thoroughly as you can to show you have negotiated in good faith and were willing to try to settle this claim yet Getty has refused provide any information. And since Getty is making the claim and sending the invoice the burden of proof rests on their shoulders not mine.
I don't understand the logic of making an offer subject to proof of claim.
The logical order of things to me would be:
1) Receive a claim from Getty.
2) Ask Getty to prove their claim.
3) If proof is received then assess what you feel is reasonable and make an offer based on the specific factors of the claim.
Would a judge penalise somebody who had taken the time to deal with the issue just because they hadn't written down arbitrary figure in a reply to a claim that had no proof?