we should say that a tab character is a delimiter between table
    cells in a manner more reminiscent of how they're used in tab
    separated value (TSV) files.

is rather abstract.  It says how we can think of a tab rather than its
effect on displaying the text on the screen.  What is meant, exactly, by
a "table cell"?  Is it a block of text 1cm wide, or something like that?

The picture on the webpage looks as though it's using tabs to do the
syntactical indentation from column 0, but spaces otherwise (e.g. for
the space between a statement and a line comment).  This isn't difficult
to achieve for CC Mode's languages (e.g. C), being a ~25 line hack.  If
that's what you want, say so, and I'll hunt out the hack.