Originally Posted by Voodoo

It's a pressure / control technique to get people to think quickly. You can refuse the search request until they get a warrant, then they will consider that "probably cause". Why wouldn't you want them rummaging through your shit? They're cops!

The "OK?" part at the end is a way to get you to think that you don't have any options. Most people don't think on their toes when in situations like that...

Example: "Just gonna take a look in your car, real quick? OK?"
Viable Response: "Actually, I don't feel comfortable with you going through my car without a warrant. Am I under arrest? If so, do you have a warrant to search my car? I may be open to you searching my belongings, but first let's talk about something else, do you mind if I record this entire process on my phone camera? I'm researching for a film that I am working on and would like to understand a little better how things work."

The things you mentioned are sales / control techniques. Most people fall for it.