I shared with them my suspicions regarding possible data manipulation, gave them the name of exchange and coin.
Now, what evidence do they want me to collect? Take a screen recording and send it to them? And then what? They will have to double check it anyway, so there is no point for me of sending them any "evidence".
It's because ordinarily, from the largest market cap website they probably received lots of reports/complaints with/without proofs. And screenshots/recordings from yours at the time of inaccuracy of data will differ from the time they will check the report(s) so that's why any services with such issue will ask for some evidence from the correspondent.
If you really care for something like that happened then you have to give such statements, else...