Can I get away with claiming I popped my tire, got some drinks, went to change it, and intended on calling someone to get me?

I got back to my car after a night of drinking. I drove about 500 feet and popped a tire. Yes, I shouldn't have been driving but we're talking about if I can beat my case based on evidence the police have. No one saw me driving but I was on the side of the road changing my tire and the police pulled up. They asked what happened and I told them I got a flat after turning the corner. They asked if I had been drinking. I said yes not specifying when. I never admitted to drinking prior to driving. Keys were not in the ignition. The car was off. To my knowledge, they have no solid basis to say I was under the influence while driving or that I was attempting to drive while under the influence. I was just fixing a tire while intoxicated about to wait for help. They forced me to take a preliminary breath test after giving me 2 field sobriety tests. I doubt I passed the one with the eyes but I know I did well on walking the line. I refused to blow into the big box.