I don't agree with the sentiment that it happens all the time (but don't disagree that it's happened more than a few times), but I do think police are much less likely to make something up if they know (and have seen) the camera evidence. No point in saying something (the day after the incident) that can so easily be contradicted later.
The police in Georgetown about half an hour north of Austin went with his gut in one murder case - "it has to be someone the victim knew" and ignored physical evidence at the scene and the eyewitness testimony of the murder victim's son. Then the prosecutor kept working against the accused for the next 25 years and suppressed evidence.
https://www.texasmonthly.com/politics/the-innocent-man-part-...
The fact that they came out with a statement instead of saying "we don't comment on ongoing investigations" makes it even more shady.