I'm not sure what the source was for that but according to the Shah's own diary (translated to English in 1874) he talks about attending a boxing match in the palace gardens on Monday 30th June 1873. A few paragraphs before sharing his thoughts on the fight he confirms being in the garden of the palace to watch the English Fire Brigade doing an exercise and so we can confidently put him in the right place and have him describing a boxing match on the 30th June. I propose the date of the fight be changed to Monday, 30th June, 1873 unless the source Boxrec has used is more reliable than the Shah's diary.
Here's a link to page 190 of the Shah's diary: https://archive.org/details/diaryofhmsh ... t/page/191 (this is within the entry for Monday 30th June as per page 189 of the diary, Tuesday 1st July 1873 starts at the bottom of page 195).
His comments on the fight I think are fascinating and you may wish to include them as a note on the fight if that's something you do:
Well; among the others came some English prize-fighters, and performed boxing. To box is to strike one another with the fists, which requires great skill and dexterity. But they wore on their hands a kind of large gloves stuffed with wool and cotton. Had they not worn these gloves, they would have killed one another. It was very ludicrous and amusing.
