I dont assume the cop in the video linked above wanted to pin something on the guy, he most likely really believed he was guilty. Thats the problem.
Cops are confronted with criminals every day and its their job to look for suspects. Its really easy to look like a nail if someone has a hammer. And once you are seen as a suspect, confirmation bias sets in. And with every word you say the risk of them finding something that looks to them like circumstantial evidence rises. Assume you said you are walking there every night, but once he specifies to yesterday you contradict yourself, because yesterday was an exception. Now add some dumb luck and you know the victim of what ever happened and you dont have an alibi. Now you returned to the crime scene, know the victim and lied to a cop.
Talking to a cop is simply reckless. They question suspects everyday and its likely your first time. You dont have to be guilty to contradict yourself in a stress situation, speech is a rather imperfect way to communicate.
And sure, they can suspect you either way, and there is nothing you can do about it except getting an attorney. Cops suspecting you of something isnt that big of an issue, there is a separation of power between executive and judiciary for a reason. Its the job of a cop to make a case against a suspect. Its the job of a judge and jury to evaluate if that actually happened.