I figure LE already had him on their radar due to behaviors at the time, but of course, they can only report incident-by-incident.
Maybe some here do not live in neighborhoods in small towns (Moscow's population is about 26,000 - the size of my hometown, which has different dynamics to larger towns). It's true that it's only 8.2 miles from Pullman, which is the same situation as my hometown (except that Hometown has no college and the college in the next town is 10 miles away).
The local police's view about late night activity is complex, IME, but tries to result in a "safe space" for students.
Late night activity is carefully watched by LE in both the small town where I live, but also in the smallish towns next door. Further, Campus Police pay even more attention to such things. Moscow PD showed its commitment in the bodycam videos released. They try to be nice, but vigilant.
Out-of-state license plates are a thing that LE watches (I know this because I teach at police academies and am active in consulting with local LE). That can work both for and against BK - but in this case, makes him come up on police radar (which might work for his defense). I believe that's why they gave him multiple messages (via SM/presser). They could see that his car fit all the markers they were seeking, but they didn't want to zero in on a person who had an innocent reason for being there.
Until his DNA showed up.
IMO.