I'm not sure that it makes any logical sense at all, to be honest.
What do your visitors gain by having to go from widgets.com to red-widgets.com?
What do you gain by having to double your marketing effort?
What does Google gain by having to sift through two sites, looking for duplicate content?
And therein lies the rub; if the new site was thingies.com, and they work with widgets, then I follow your logic - and so, I think, would Google.
But unless you are removing red widgets from widgets.com to red-widgets.com, then you may have dupicate content issues compounded by 'link farm' issues. There's no evidence to suggest that Google really cares who owns a site (you could own two sites and have completely different whois info).
And there's little evidence to say Google would mind a bit of reciprocal linking - on a small, intimate, candle-lit basis ;)
But once you add duplicate content issues, the Intiminate Deal For Two may lead to marital breakdown.
Translation: It looks like red-widgets.com is there to promote widgets.com, and is not really serving your visitors at all - from Google's perspective. Much better to go for widgets.com/red-widgets/ - and why not?