Is this an MSPA member company? From what you are saying, there is not question regarding the acceptability of the report you provided, there is no question regarding fraudulent behavior on your part, there is no question regarding your performance of the shop, just an employee accusation that they spotted you because you were looking at their name tag. Since when are name tags not to be looked at? It sounds to me, from what you have stated, that you are entitled to 100% payment and reimbursement and it would be unethical for the company to do otherwise.
When companies take on clients they are not free of all risk from their clients. And yes, I know, that many of them want to leave the shopper hanging in the wind if the client does not pay. But that does not mean that the shopper needs to be the one picking up the tab--especially when the shopper performed what they were required to perform, in the manner they were instructed to perform it and reported it in a timely fashion accordingly. You may be willing to take some of a loss, but since the company evidently does not have adequate contracts with their client to prevent such situations, you should hardly be eating much, if any, of the loss.
While I would give the company a little leeway to work this out and thank them for the 'heads up' that there may be a problem, I would also make it perfectly clear to them that they need to work it out with their client. In a hotel/resort setting it is a fairly minor loss the client would take by backing out the charges. Somebody with the company should be negotiating that with the client even if the client does not ever pay for the shop. Far better to have your loss only the fee from the shop rather than the whole expense.