Balance Transfer Incompatible

I was looking for a 0% card to transfer a balance from an American Express account and a MSE soft search indicated I had a 90% chance of being accepted for the Sainsbury's 29 month 0% interest credit card.

I completed an application for this card and was successful, only to discover after completing the application that Sainsbury's cards are not compatible with Amex for balance transfers. I had no other use for the card so declined to accept the card. Upon speaking with a representative from Sainsbury's I was told that certain types of Amex card are not compatible while others are but that it's not possible to indicate this before the application stage. I was offered no explanation as to why this is the case, despite asking repeatedly. Furthermore I was told that this would still count as a hard search on my credit report and that nothing could be done to change this (I knew this was the case when I applied: but my assumption would be that the product would be worth it - I didn't envisage having to apply for another product for the same purpose, which I now will have to).

It seems to me to be incredibly unfair (and misleading on the part of Sainsbury's) that customers can be landed with a hard search record for a product that is totally useless to them and for which they would not have applied if all the information were available to them. My application was not rejected, but it will still be recorded and may impact my ability to get credit elsewhere. I would not have considered applying in advance had I known the product would be unfit for my intended purpose.

Is there anything that can be done about this? I presume not, but it would be useful to know in any case.

Many thanks.