They'll print what they like regardless of whether you talk to them or not.
Local rag journos aren't generally all that bright, are they ... otherwise ... they wouldn't be local rag journos, would they.
And even if the journo gets it right - and you do get some good ones - the subs will think it doesn't make a good enough story and will mangle it at worst, or put on a completely nonsensical headline at best.
As a politician I do have to stay on speaking terms with the local press (well, in the longer term that is, there was a period of a few months when I made it clear I wasn't talking to them over something they'd misrepresented even more egregiously than usual) so I usually put some effort into telling them the real story in the hope that some of it might make it into print or onto the airwaves, and I think that on balance, in the long run, this does more good than harm.
But I can't tell you which way to jump with a one-off encounter with them. Could go either way, pretty well at random.