Yes, assuming the closures coincided with where there was tape. It doesn't seem like that large an area; given that for serious fires there are usually a number of fire trucks and ancillary vehicles, plus law enforcement and EMTs, plus lookey-loos and press, I'm sort of surprised that he would have been able to park within that area over an hour after the fire started.
Also, there was construction work already going on (I think on Garfield) which would have reduced the amount of parking nearby, rush hour parking restrictions on some streets (Cleveland, but not until 4:00) one side parking on several of the streets (including Woodland), etc. It was already not an ideal situation to find parking that day, so the addition of the fire/LE equipment vehicles would have made it even more difficult. Looking at the parking signs on google maps reminded me that there are signs posted all over the neighborhood warning that the neighborhood is patrolled by private security. Who would break into a house in the middle of the day in this neighborhood?! Crazy! I guess LE has already looked into the guy/gal on patrol that day/night/day. I know whenever I have my locks changed, I feel like I want to have them changed again so the locksmith doesn't have a key copy. Sometimes people who work in security seem to have knowledge accrued from the other side of the coin, to mix my metaphors. Remember the guy who was selling home alarm systems and was raping women in the neighborhood to boost sales?!