Trespassing is generally not a crime unless there is a clear indication that the person committing it should not go there, such as a fence or a sign or some form of explicit communication from the property owner. The fence or sign doesn't have to make it impossible for the person to access the property, but it does have to be there so that it is clear that they shouldn't enter the property.
The Internet should be treated the same. Anything put on the Internet should be presumed to be public unless there is some indication to the contrary.
In this case, most of the information he accessed was clearly intended to be public, so there was no reasonable way for him to know that there was some private information improperly co-mingled with the public information, so he can't be faulted for not realizing that he shouldn't have accessed some of the information.