I think those techniques may be for neutralising the chlorine. They may not remove the Cl from water but change its form. More active compound turns into more neutral forms.
I found this web page after a quick search;
http://www.fs.fed.us/t-d/pubs/html/05231301/05231301.html
Hypochlorous acid (HOCl) found in bleaches and water treatment chemicals (I don't think there's HOCl in mineral waters) gives these reactions with Vitamin C.
C[SUB]5[/SUB]
H[SUB]5[/SUB]
O[SUB]5[/SUB]
CH[SUB]2[/SUB]
OH + HOCl → C[SUB]5[/SUB]
H[SUB]3[/SUB]
O[SUB]5[/SUB]
CH[SUB]2[/SUB]
OH + HCl + H[SUB]2[/SUB]
O
(Ascorbic acid)
C[SUB]5[/SUB]
H[SUB]5[/SUB]
O[SUB]5[/SUB]
CH[SUB]2[/SUB]
ONa + HOCl → C[SUB]5[/SUB]
H[SUB]3[/SUB]
O[SUB]5[/SUB]
CH[SUB]2[/SUB]
OH + NaCl + H[SUB]2[/SUB]
O
(Sodium ascorbate)
As you see, there's still Cl in water (form of NaCl and HCl).
So these methods are for eliminating the HOCl (bleach, disinfectant etc) in the water. Cl remains in the water but in a less effective form.
But, I don't know how those guys (in the link above) found 0 mg/l Total Chlorine content in the Vitamin C treated water.