I used to live and work in this area for several years, including right behind the NKC Quiktrip, downtown next to the Quaff, and for a short period of time, close to Southwest Blvd.
There a few a few things I will note as a point of information to those sleuthers out there:
1) North Kansas City police offers pull people over all the time. I think I was pulled over 3 times on Burlington, all three times pretty close to the Quicktrip. The officers were generally fairly nice in dealing with me. I never felt endangered.
2) I always felt very safe at the NKC Quicktrip. It is very clean, open 24 hours, staff always there, bright lights on, ect. Often times officers would hang out there and were very friendly with the clerks. This is one of the safest gas stations in the KC area. I can't same the same for the gas stations downtown or further south. I always tried my best to avoid getting gas downtown. In fact, when I lived downtown, I typically would use the NKC quick trip as it was close to work. If she lived downtown, she may have been doing the same.
3) NKC cops rare drive outside of their jurisdiction. They are also not suppose to pull anyone over outside of jurisdiction. Search "North Kansas City" on Google maps to see what the jurisdiction covers. It does not cross the river.
4) Southwest Blvd is on the other side of downtown. You can take 9 straight to it. Route 9 (which is Burlington) turns into Broadway street , which hits Southwest Blvd at the end of downtown. If you head west, you travel into a large mexican area with plenty of mexican restaurants. If you continue down the road you will be just west of westport and eventually cross over to KS. I personally did not like that area and did not feel safe over there.
5) It is very atypical to get pulled over on 26th street. It is more common to pull someone over on Burlington. There is plenty of room to pull over. If she was heading north on Burlington, my only suspicion is that she there to get gas. There isn't much else for a 20 year old to do further north of QT. You have to be 21 to get into Argosy.