Demat a/c is no way a compulsory requirement for mutual funds as of now. And it seems you wanted to trade in ETFs as well which requires demat. If you want to deal in mutual funds it does not need demat. It's highly possible you might have said anything regarding demat/etf and fundsindia customer care told you about having one with them.
When I opened my a/c I was just checking fundsindia for New Pension Scheme (NPS) payment. I found out after making a/c that NPS needs ECS thus my opening of a/c was of no use as I already have ECS with my current SBI Bank. I wanted to pay premium as and when suitable time comes just like opening SIP and using addtional investment or redemptions available in fundsindia's SIP. Next day I got a call from fundsindia that they are waiting for my form. I made excuse of sending courier yesterday itself.
Meanwhile I was using my mother's a/c of kotak security for mutual funds. Since my mother wanted to transfer all unit holdings in my name and since I had a gut feeling that market is going to fall anytime in begining of new year I redeemed all units and closed kotak a/c. So I needed an a/c for mutual fund. Meanwhile I was making excuses of courier being sent, wrong address, my form got lost etc to avoid fundsindia. Later I thought it's just 50 bucks to send a form so let it be, in mean time I can use them instead of Zerodha which kept promising mutual funds service will begin "soon".
I sent my forms, it reached on time and my a/c was opened. On further exploring fundsindia I found out it has so many interactive features. My 1st few "trades" were profitable and thus I sticked to fundsindia and stopped bugging zerodha for mutal fund service which is still not fulfilled by zerodha. 1 day I asked them for ETFs as Nasdaq 100 was open for NFO, they told demat is required which has demat charges and broking charges which I found out very high priced hence I skipped idea of opening demat with them or emkay. That time also fundsindia told demat is not required until I wish to trade in stocks or etfs.
Hope it helps.