If a problem is created by fibres from the tampon being left inside a woman after the tampon's removal, then an all-cotton tampon is going to create more of a problem, not less . Run a cotton T-shirt through one dryer and a rayon blouse through another. Ignoring for the moment the sideways logic of this badly-expressed bit of the scarelore, if the use of rayon in feminine products is something to be wary of, it's for an entirely different reason. Dioxins are produced through the chlorine bleaching of wood pulp. The chlorine used to produce rayon results in additional dioxin.
Rayon means more dioxin.
If dioxin is bad, then you'd want to eschew rayon as well. The first tampon was introduced into the American market in 1933 by Earl Haas, who developed it for his ballerina wife. At the time, the tampon was all-cotton. Environmentalists were also concerned that the bleaching process could leave traces of harmful, highly toxic dioxins in women's bodies. After a rash of TSS deaths in 1980 and two 1985 U.S. studies linking TSS to tampon use, manufacturers began removing most of the chemicals.