getting a 'high' zinc result would really all depend on what boundaries the specific lab sets around 'normal'. i've seen everything from 14 to 19.1 set as the top end.
as for whether zinc might be the only reason for low testosterone, i did a generic scholar search on low testosterone and nutrition deficiency and on the surface it's all zinc and possible correlations with vit d3 status (which would make sense since zinc is an important cofactor)
this looked interesting:
Low testosterone levels are common and associated with insulin resistance in men with diabeteshttp://www.ncbi.nlm.nih.gov/pubmed/18319314
low zinc is definitely associated with insulin resistance, but so is magnesium so had a look at mag and testosterone. the results sort of shifted over to studies in postmenopausal women.
given that zinc is such an established known when it comes to reproductive health, plus the links between low testosterone and other health issues that also involve low zinc, i'm thinking that optimizing zinc would be your 'occam's razor' kind of approach. then, once zinc deficit has been ruled out as a factor, one might look for other possible causes of subpar testosterone status.
The role of zinc in reproductionhttp://link.springer.com/article/10.1007/BF02784623
Zinc is a very important element in the reproductive cycle of species. In humans, it is necessary for the formation and maturation of spermatozoa, for ovulation, and for fertilization. During pregnancy, zinc deficiency causes a number of anomalies: spontaneous abortion, pregnancy-related toxemia, extended pregnancy or prematurity, malformations, and retarded growth. Delivery is adversely affected by deficiency. These different effects of zinc can be explained by its multiple action on the metabolism of androgen hormones, estrogen and progesterone, together with the prostaglandins. Nuclear receptors for steroids are all zinc finger proteins. Zinc supplementation has already proven beneficial in male sterility and in reducing complications during pregnancy. However, it would be worth conducting larger-scale trials to confirm these beneficial effects.