If you're going to job shop, all parties understand it's done discreetly. There are feelers flying around all the time through one back channel or another. That certainly didn't happen here.
Once the news comes out, there are ways it gets handled. If you're just listening out of respect, there is a degree of media statement used to express that. If media wrongly ties you to jobs, there are denials. We see this stuff play out all the time.
Was coen actively pursuing all those jobs? Probably not all but surely most. think the reports were accurate enough he couldn't afford to speak on the one or two that weren't, because it just validated the other reports.
So yes there is more than ample deductive reasoning to point to him pursuing these jobs. The entire thing was poorly handled.
If he has a desire to be a head coach, college or NFL, a 3 year contract isn't going to deter him from climbing what he sees as an upgrade. But I don't think the news of him looking at an NFL position came from him, Sexton maybe but not Coen.