What makes this different? When one character appears in a second's strip, there's an implication that the two strips share the same universe (or at least part of it). So, for example, because Dilbert is shown in Blondie's shop, that it's located in the same unnamed city as Dilbert's unnamed company. Or that because Walt Wallet dropped in to visit Dick Tracy, that the events in Gasoline Alley occur in the same universe as those in Dick Tracy. (See: Blondie Cameo and The Alley Comes to Tracy)
The point is, when one character appears in another strip, then both share the same reality. Jef Mallet chose to do something different in Frazz. Caulfield says he's reading a "Big Nate" collection. So in Frazz's world, Lincoln Peirce's character isn't a real person -- he's a fictional comic strip character (just as he is in real life -- if you really think about it).
And just for the record, here's what was happening in the fictional world of Big Nate that same day.