Sure, putting all your money into a single asset may have a higher degree of risk if you aren't fully aware of what is happening with that asset (eg internal fraud or mismanagement or other issues which may have a fatal impact on the viability of the company).

If you are going to gear your investments to a high level, you'd want to make sure you have a degree of diversity built in that will allow for the occasional "dud" investment. Investing in a fund which chooses from 10+ blue chip shares is unlikely to have a serious long term impact if one of those shares were to go bust.

I don't think it's necessary to invest in an index to get the diversification you need - an index will simply average your returns across a much larger selection.