I'd say, "botched," is probably too strong a word and the record that we have to go on now, is obviously less than complete. Fuhrman is regularly criticized for "Monday morning quarterbacking," but IMHO that criticism comes from those unfamiliar with police work. The cops that were dispatched to the scene arrived after the paramedics appeared to be in control of the situation and there were no apparent signs of struggle (though Fuhrman points out there is generally, by all accounts a missing 40 minutes).
I can not characterize the cops as having "botched," any potential investigation, and perhaps the best parallel I can draw is that there are things they probably should have done at the scene or at the hospital, just like you should do a complete walk-around of your car and visually check all four tires before you drive anywhere. Of course, very few people actually do this and hop in assuming the tires are in good condition unless there is something very obviously wrong, and most of the time they're right. If the responding officers were negligent, it was the type of negligence probably more than 75% or better (my guess) of patrol officers would have made under the circumstances.