Of course, with an interest-only mortgage, yes one would need to be cash-flow positive, because there is no such thing as gaining equity. Again, my understanding is that such properties are extremely rare.
When I say you "always want a mortgage" I mean that if you have a mortgage you have your tenants paying for the house. Your cash on cash return is far higher. If your potential property doesn't support that, then find another property. Paying $200k cash for a house that nets $500 per month is far less interesting than buying 10 houses at $20k down that each net $200 per month -- and it takes exactly the same cash.
EDIT: Here's a fun Reddit thread on the topic:
https://www.reddit.com/r/RealEstate/comments/36ikp6/landlord...
Here's an example from that thread on how quickly the math takes you to roughly cash-flow neutral -- and this is with 25% down and 1% rental price:
https://www.reddit.com/r/RealEstate/comments/36ikp6/landlord...