Insider trade on Splunk acquisition?

I know this isn't what happened, but what if one day I'm waiting for the bus and I over hear a guy talking on their phone about an imminent acquisition?

1. Would that still fall under insider trading even if the information was accidentally heard, and even if I wasn't 100% sure of its accuracy?

2. If I had no clear connection to the company how would it be proven that I was trading on insider information? Surely it's not enough just to say the trade was statistically unlikely, or is it?

It's still not public information (e.g. "Material Nonpublic Information"). You can't trade on it.

See 17 CFR § 240.10b5-1 "Trading “on the basis of” material nonpublic information in insider trading cases", particularly section (b) "Awareness of material nonpublic information."

https://www.law.cornell.edu/cfr/text/17/240.10b5-1

disagree, the SEC has lost a lot of cases on this idea

if you’re not affiliated with the company and simply overhear and trade, make enough to retain a lawyer real quick