My understanding is that investment funds are separate trading entites from their promoters. So even though a bank might sell the funds to their customers, or perhaps own the fund manager, the assets of the fund would be separate from the assets of the bank itself.
Thanks guys for the response,this also was my understanding and makes sense.However I am fortunate enough to have substantial funds invested with one particular bank,was considering adding to it shortly but am wary until I get a definitive answer.