Paranoid rubbish.
There are two major problems with this story.
(1) You have to be successfully sued for something. While the U.S. is certainly a litigous country you can't just sue people you don't know for no cause and win huge amounts of money.
(2) Even if you discount the first point a house is still just another asset. So if you had a mortgage for $100,000 and $100,000 invested elsewhere that asset is no more or less protected than your house.
I would surmise that short of pulling your leg your real-estate source is confused about stories involving identity theft. To some degree a larger mortgage may protect you from identity thieves borrowing on your house and sticking you with the bill. However one should note the use of the
word may. If someone has stolen your identity you are going to have problems regardless.
Here is what the Federal Trade Commission has on identity theft (how to prevent it and what to do if you think it has happened)
http://www.consumer.gov/idtheft/ But if you are still worried about being sued because you don't have a mortgage
you should talk to a lawyer or even your accountant.