I think that the disconnect is that you are thinking about strength in more reductive terms than I am in this context, perhaps thinking about it in terms of neural drive & central motor command, recruitment, voluntary activation. Of course, testosterone does augment these too [1], but in this context I refer to strength as a product also of increased muscle size, because increased fCSA (fibre cross-sectional area) is an important contributor to increased strength. For that, just take Bhasin's 1996 study [2] showing effects of testosterone enanthate + training on muscle size & strength).
These are direct muscle anabolic & rapid nongenomic neural effects rather than indirect ones that arise from enhanced recovery from intensive muscular work.
[1] Felici, F., Bazzucchi, I., Sgrò, P., Quinzi, F., Conti, A., Aversa, A., … Di Luigi, L. (2016). Acute severe male hypo-testosteronemia affects central motor command in humans. Journal of Electromyography and Kinesiology, 28, 184–192. doi:10.1016/j.jelekin.2015.12.004
[2] Bhasin, S., Storer, T. W., Berman, N., Callegari, C., Clevenger, B., Phillips, J., … Casaburi, R. (1996). The Effects of Supraphysiologic Doses of Testosterone on Muscle Size and Strength in Normal Men. New England Journal of Medicine, 335(1), 1–7. doi:10.1056/nejm199607043350101