Correct, to avail the HSBC Premier card you need their premier account status.
Good thing is they're very transparent with this, you can find the details on their page itself:
https://www.hsbc.co.in/premier/.
It doesn't explicitly say about investments but highly unlikely that you can just show your HSBC MF investments and get this status. Maybe through FD of 40L or something it might work.
Just FYI - this card not free. You pay 12K + GST as joining fee and in return, you don't get any points. But you get 12K Taj gift card & their epicure membership (this is not with 1 free night stay). The value on joining fee is not that great, I think. But yes if you're planning to stay at Taj in an year or so then this is pretty good. Other benefits I guess you already know.