Missing bag report swindle

I have just had the worst customer experience with a major airline in my life and want to know if there is anything I can do.

TL; DR:

I got my bag one day late, after that I was told by employees of the airline I flew with (British Airlines) that I "do not need to file a missing bag report because the missing bag is already in the database". After that, I requested an expense reimbursement, and the answer was basically "we cannot reimburse you because without the missing bag report, there is no way to know if your bag was missing" which in my opinion, is pure BS.

Here is the whole story:

• Day 1: I flew from my home airport to my destination. My flight landed late, at 7PM local time, at which point I had to go pick up my bags. After waiting for them for 30 minutes, it was clear my bags did not arrive with my flight. An employee of the airport told me he will call someone from the airline company to help me. After 30 minutes, he came back and told me there is nobody in the office, and that I should just go to the check-in counter to talk to the airline people directly. However, border control took a long time, and by the time I got to the checking counter, it was empty. I could not contact anyone from the airline company, and was told to call them on the airport phone. The phone redirected me to a call centre which could not help me and told me to come back the next day.
• Day 2: I came back to the airport at the time I was told, but the checkin counter was still empty due to a canceled flight. After 5 hours, I was finally able to talk to an employee of the airline I was flying with. After being insulted and shouted at (why didn't you contact us yesterday? I did, but there was nobody here that's not true Yes it is. No that's not true, there's always an employee here Well there wasn't yesterday. I don't believe you) I was told that my bag is already en route to the airport and it will arrive in 1 hour. I got the bag after 1 hour, but by that time, several expenses (for example, parking at the airport for several hours and driving to the airport and back) were already caused by the delayed bag. I asked the clerk what I need to do to get refunded. They told me to just go to the website and fill out the form, saying "the fact that your bag was delayed is already in our database"

• Days 3-now: I filed the reimbursement form explaining all the costs that were incurred by the delayed bag. The answer from the airline was that I need to give them the "delayed bag report number". I explained to them that there is no delayed bag report because I was told (by them) that I do not need it. Now, the answer from the airline is that they will not process my claim because there is no missing bag report:

  As previously mentioned, we need these delayed baggage reports in order to trace all missing bags and have control & records of all missing bags and I hope you’ll understand we have to be consistent so we’re fair to all of our customers. This means we can’t make an exception this time and make any compensation payment without such a number and I’m so sorry to let you down.

My question is this:

Can they really do that? Note: I did nothing else but what the airline told me. I followed their instructions to the letter. They themselves told me to not file a report because they already have the missing bag in the database, and now they won't process me because there is no report?

Edit:

The airport I flew into was San Francisco International. I flew from Venice to SFO via London, and the flight where the bags were lost is the last one.

The airline I flew with is British Airways.