Because they knew who he was and had eyes on him.
BAU probably profiled him as well. And they were right about him, as far as we know.
Well, yes and no. At the time they said "approximate time of death" was 3-4, they might already have known it was later - maybe not. Maybe that was in fact the first guess and they just let it hang out there.
We now know they had plates and DMV records on the car, but it wasn't a 2011-2013 Elantra. It was 2015. Etc. AFAIK, they did not correct that. Not that most people can tell model years on sight, but still.
IOW, when they made some original statements that the public took as facts, they later learned something else (very quickly too) but did not rescind or correct the original information. For good reasons.
And they don't have to. But some would say that's "misrepresenting," I think.
As a teacher, I don't think it would be an easy sell to today's students to try and convince them (I typically start with videos of various mammals performing these actions, as all mammalian brains have similar wiring in this regard). Flight means "run away." In fact, there are posters in my classroom outlining one's choices in case an assailant attacks us:
1) Hide/freeze under the desks
2) Run away/flight
3) Find an object and fight
These are illustrated by pictures, of course. I always add: think about using furniture in a more creative way than just hiding (such as blockading/obstructing). I also ask how many people have a weapon with them, with interesting results (they are not supposed to have guns, btw - and sometimes a person will still reveal they have one with them). Mostly it's knives, pepper spray, bear spray, and sometimes, even, hair spray (which in a pinch can be weaponized).
I also point out that several doors in my main classroom do not open without a key (which is something I've complained about over and over, and ask them to watch while I demonstrate which doors can be opened from the inside and which cannot). The ones that don't open are class and can be broken from the outside by an assailant with a gun, but they are fairly sturdy and no one anyone could break them easily with anything less than gunfire, IMO.
I then tell them that sitting nearer to an operable door is a good tactic (this changes nothing about where they sit, though - not once). All of them tend to choose their seats on first day, and with rare exceptions, do not change where they sit. They cannot give me their reasoning on this. Or won't tell me, one or the other - I think they would if they could though, as they look thoughtful during the discussion. If you have students in your family, please talk to them.
I have been shocked by all the self-reports of U of ID parents in various places saying that they have not mentioned the murders to their vacationing students, for fear of "worrying them" or '"triggering them." A little worry can be a good thing and if a student is so fragile that they cannot handle a parent's words on such matters, I have no clue how they're handling college professors and the signage and the lessons on "active shooter procedures" that most schools - even elementary schools - are practicing.
I hope everyone talks safety with their families - one more time. Cameras. Cameras are very good.