I used to believe that the "vice" in "vice squad" had the same kind of meaning as that in "vice president", so that a vice squad would be an alternate squad that would stand in for some main squad when the main squad was unavailable for any reason.
A childhood belief about police

others believed things like this
- I used to believe that the loser of the Presidential election became the VICE President. — AirInSea
- My 18 year old brother thought the former vice president was named Al Gorbachov.— Jeff
- i used to think that if you were a boy your younger sibling would have to be a sister and vice verca (sp?)— ben
- when i was little thought that ants changed traffic lights from green to red and vice versa.Anon
- All colleges had campuses in the state of Maine not just a main campus. — Michael
- I always believed that we lived in Manchester (we didn't) but it was always the main place on the local news!— Richard M