Certainly an oxidizer can take out color, but only on uncontrolled situations. The mark of a professional is to control the situation.
Without much in the way of exceptions, a formula made for carpet stain removal is completely safe when used according to proper procedures. Where cleaners get into trouble is when they take the chemistry in their own hands and lose control of the oxidation stain removal process. Mixing highly concentrated hydrogen peroxide with an accelerator is very risky. That is the number one reason to use a branded product designed for safe carpet stain removal. Also, only use products designed for the carpet type (e.g. Stain Magic for Wool, on wool fibers). You just don't see people getting into trouble, using proper procedure.
The only time you should really pull color is when the dye is irreparably damaged by the stain material, such as old dog urine on a wool rug. In these cases, even plain water will draw out color.
Now, there are rare exceptions to the rule of Oxy first, but it is usually used when you know more specifics about the stain element, fiber type and condition of the fibers. These are best covered at length in a stain removal class.