It seems that 「か」 in this case may be an indication of uncertainty about the situation, so maybe a similar feeling to what "purportedly", "allegedly", and so on would convey. Sometimes DeepL leaves out important context like that in favor of a more natural translation, I feel. I'm not a Japanese expert, so I hope you'll listen to a more advanced person on here who has experience answering these questions, if someone else answers!
This is my first answer on here, so sorry if I didn't do too good 😅 I wanted to write a comment instead since I'm not quite sure of the answer, but it requires 50 reputation. Guess I'm trying to build it up somehow, but this might be an utter failure and I might be completely wrong, who knows!