This isn't true.
A person can break into your home, fall down stairs and file a lawsuit against you.
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In the Northern New England states (VT/NH/ME) that have a sort of freedom to roam codified in law (basically - unposted, undeveloped property is generally free to access for low-impact uses like hiking without requiring permission) - there is broad liability protection provided to the property owner.
For example, the law in VT for liability in that land access situation is only if the injury that occurs is "....the result of the willful or wanton misconduct of the owner." (and has further exemptions from even that if the injury is with regards to accessing equipment/machinery/personal property - which you're not entitled to access).
You pretty much need to be setting traps or creating some truly absurd unnatural hazards to be at legal risk.
What I did look up:
"Premises liability laws generally do not extend to trespassers, such as burglars, because they do not have a legal right to be on the property. However, property owners in California may be liable for injuries caused by a crime on their property if they should have reasonably foreseen the crime and failed to take steps to reduce the risk. This is known as negligent security and can apply to crimes such as burglary, theft, and robbery. Factors that may contribute to a negligent security claim include: Broken or missing surveillance cameras, Lack of security guards, and Broken or inadequate locks."