That case refers to a company defrauding its own shareholders by withholding material information from them during a buyback.

That's far different from what OP is suggesting -- a wink/nod to a third party indicating to buy or sell.

No, that's precisely what insider trading is--trading by any person based on inside information they have acquired through means covered by a fiduciary obligation (i.e. employment, service provider, etc.).

A company can trade on inside information with its own shareholders, since the company is using information it has access to which its own shareholders may not.

Exactly. It's not "trading by any person". Insider trading is can only be done by someone with a fiduciary responsibility.

If a non-involved person somehow acquires "inside" information (without getting it from one with a fiduciary responsibility) it's not insider trading even if the information is non-public.