Living off of the interest is just a lazy way of stating that your investments can cover your spending perpetually. It doesn't really matter if you've got rental properties, bonds, CDs, stocks, or whatever. If the mix of their earnings + growth covers your spending amounts, then you're living off the interest.
If you buy a good index fund, say
VTSAX, it will kick off 1.86% in dividend payments, and you can sell appreciated shares to make up for the remainder of your needed funds.
For the record, dividends aren't "free money", and there's basically no difference between collecting a dividend and selling an equivalent amount of shares. This is because the stock price actually drops by the dividend payout amount.
Example:
You have $100 worth of stock, it pays a 5% dividend, you now have $5 in your pocket and your stock is worth $95
You have $100 worth of stock, it pays no dividend, you sell $5 worth, you now have $5 in your pocket and your remaining stock is worth $95
I'd also recommend reading the Jim Collins posts that
kendallf posted above.