Actually, I think it's the same cap except one is beat to $&!^. In your photo, you can see the tool marks in the new one which have resolved in exactly the places as the old one, just not as deep.
Answer -- it was the cap. And now you have a complete valve if you ever want to replace any other parts except the float. For that price, I'm guessing they sold you the white-cap 528, but all you needed was the cap. If you got a 528MP, then you got a really good price.
I'm so happy we were able to get you back in business with a relatively-minimal hassle. Now that you're up and working, you can still consider reporting the failure to Toto and seeing if they'll send you a new valve; that way you can put it in the drawer until next time. Taking the whole valve out actually is pretty easy, you usually can unscrew the mounting nut on the old one by hand or with one application of pliers, and then you have everything new when you put in the new one. Toto customer service is at 1-888-295-8134. Note it's an 888 number not 800.