First of all, the study he cited was not funded by the NIH, at all.
Second, drug discovery research absolutely cannot be done without some degree of animal testing. The FDA even requires it. Sure, cell based models ("in vitro" experiments) and computer modeling are done up front, extensively. This eliminates many toxic compounds, which is a great thing. But such studies are inadequate to predict fully how a mammal will respond to a medicine.
By and large the approved and approvable experiments are dose-ranging and safety experiments, such as giving mice varying amounts of a proposed drug and determining its half-life, what tissues it goes to, its route of elimination (e.g., urine, feces, is the molecule intact or metabolized, and metabolized to what). Every such experiment is overseen by on-site veterinarians, is limited in size to the minimum number of animals needed to get a statistically meaningful result, and there is a book-sized list of animal care protocols to follow, from feeding schedule, to cage size, to diet, to provided exercise time, socialization, etc.
When you have data on two non-human species (say, mice and guinea pigs) you are able to statistically model with some confidence what human doses to use in a phase I clinical trial and what issues to look out for (eg., elevated liver enzymes, renal problems, GI issues, etc.).
The FDA simply will not allow any human clinical trial until such animal modeling is done. If you want drugs, for now anyway, animal testing must be done.
This is speaking from 35 years as a drug discovery scientist, half in pharma.
