The sold price should show in the order details, despite any apparent glitch with the best offer feature.

It's more than likely a timing issue - I had something like that once. I had set up a custom listing for a buyer, which was for a bulk quantity of a couple of different items. I worked out the pricing on each item, added them all up, and set the BIN price.

I then had this notion I had put the wrong price in and that I had incorrectly charged twice as much as my original quote for one of the items, so went to revise the listing as quickly as I could (since I'd already sent the buyer the link), and reduced the price. A few seconds after I submitted the revision, I got the 'item sold' notification, and at that point I realised my original (higher) price was the correct one. 

On my eBay page, the order details showed it sold for the lowered price, so I was all set to just wear it, but then I got the PayPal notification and it was for the full, original amount - somehow, I must have submitted the revision at the same time they were purchasing, or perhaps they had the item in the cart at the original price, which didn't update when they paid.