It appears that most shampoos do not cause this. However, shampoos with with selenium sulfide will indeed increase oiliness.
From Pierard-Franchimont, C. Arrese, J. E. Pierard, G. E., Sebum flow dynamics and antidandruff shampoos, JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS, VOL 48; NUMBER 2, pages 117-122 (1997).
"It has been previously shown that excessive oiliness is a disturbing side effect following regular use of selenium sulfide shampoo to control dandruff (4,5)"
"s. Many studies have shown that the early sebum flow after the skin is cleaned comes mainly from a reservoir in the pilosebaceous follicle, and not from any feedback stimulation of the sebaceous gland (13-15)"
"In the present study, most of the antidandruff shampoos showed an absence of significant
SER change over time....Such a finding confirms the unreality of the so-called reactive seborrhea, in which the sebaceous excretion increases with the frequency of most hair washes"
"(4) H. Goldschmidt and A.M. Kligman, Increased sebum secretion following selenium sulfide shampoos, Acta Dermatol. Venereol., 48, 488-491 (1968).
(5) G. E. Piérard, C. Piérard-Franchimont, and T. Ben Mosbah, Les pityrosporoses. Pityriasis versicolor, folliculite pityrosporique, dermatite séborrhéique et état pelliculaire, Rev. Med. LiPge, 44, 267-271 (1989)."
"(13) A.M. Kligman and W. B. Shelley, An investigation into the biology of the sebaceous gland,.]. Invest. Dermatol., 30, 99-125 (1958).
(14) J. S. Strauss, D. T. Downing, and M. E. Stewart, Sebum secretion rates in relation to age, J. AppL CosmetoL, 3, 257-266 (1985).
(15) C. Pirard-Franchimont, G. E. Pirard, and A. Kligman, Seasonal modulation of the sebum excretion, Dermatologica, 181, 21-22 (1990)"