Your interesting question sent me looking for empirical basis for the advice not to bite the child who has bitten someone. I've found it challenging to trace this back to empirical work.
A featured article published in 2011 by the American Psychological Association, Biting questions, stated:
One intervention to absolutely avoid is biting children back, a technique some adults did in the past, child psychology experts agree. Some thought that you could discourage biting by showing kids just how much it hurts. “But, really, what biting back does is model the very behavior you’re trying to extinguish,” says [John] Marr, [PhD, professor emeritus of psychology at the University of Arkansas]. “Kids this age are sponges for various types of social learning, and they don’t yet have the problem-solving and social skills to avoid biting. It’s up to adults to show them the right ones.” [...]
Clinical psychologists can find themselves on the receiving end of these concerns, and look to their colleagues for answers. There’s scant research on toddler biting because it’s not easy to study in a lab, but child psychologists have found that some techniques work well with biting. The short version? Turn down the anger, shame and embarrassment, and tune into toddlers on their own developmental level [emphasis added].
The fundamental principles underlying the advice appear to be:
"Do as I say, not as I do" doesn't work well. It could actually reinforce the undesired behavior; at the very least, it's confusing.
Two-year-olds are limited in their understanding, self-expression, and self-control.
An additional factor may have been a 1980 article by Schmitz and ten Bensel, The Biting Child Syndrome, about a supposed correlation between a child biting others and the child being him or herself the victim of child abuse. It appears to have had a certain influence on other researchers' thinking. (Note, the Schmitz and ten Bensel article was based simply on two case studies, which makes it surprising that their article had so much impact. Here's a typical citation of their work:
Still another rationale for biting behavior is provided by Schmitz and ten Bensel (1980) who postulate that
there is a relationship between biting behavior in
preschool children and their being victims of child abuse.
Aggressive biting, according to Schmitz and ten Bensel,
may mean that a child has been a victim of aggressive
acts or an observer in an aggressive environment.
Caution should be used, however, when qualifying biters
as victims of abuse. Biting alone may not be a sign of
abuse but should be considered along with other symptoms and behaviors consistent with an abused child.
Developmentally, one can theorize that biting has
two origins. It is widely viewed as a part of "normal"
development. However, when high frequency or intensity of biting behavior is present, it may be viewed as "dysfunctional." In these instances, biting behavior may indicate sensory integration difficulties or possible child
abuse. Schmitz and ten Bensel (1980) advocate for better
observation and documentation of biting behavior so that
more clear distinctions between "dysfunctional" and
"normal" biting can be made. Certainly, the literature on
biting behavior supports their request for better documentation of the incidence of biting, including the context of when and where the incident occurs, precipitating
and resulting factors, and behavioral consequences. (de Atiles, Stegelin, Long,"Biting Behaviors Among Preschoolers: A Review of the Literature and Survey of Practitioners." Early Childhood Education Journal. 1997.)
Bottom line: I don't think there have been any empirical studies about the specific intervention you described.
Edit: I forgot to say, I did find one recent article which did have some actual data, but it wasn't from a controlled experiment, and it wasn't testing the intervention you described.
The authors view biting behavior as a toddler's developmental
need for oral sensory stimulation. In their tests, the incidence of biting were decreased by offering appropriate alternatives for chewing stimulation.