You are talking about unkeyed collision resistant cryptographic hashes. Which make collisions expensive to find. The article is about a different kind of hash,

You are talking about unkeyed collision resistant cryptographic hashes. Which make collisions expensive to find. The article is about a different kind of hash, namely keyed universal hashes. The idea behind a universal hash is that for any two distinct messages, the hash will only collide for a negligible fraction of keys. This is an absolute mathematical property, so it holds even against computationally unbounded adversaries. Such a function can be used to construct MACs/PRFs, such as GHash or Poly1305.