I don't think it's advocating for doing a single pushup. Seems to be about the idea of simple physical tests (walking speed, number of pushups in a minute, grip strength) being better predictors of health than BMI.
For things like walking speed, it's a little harder to game it without actually increasing your cardiovascular health. But without knowing why something is a proxy, it might be useless/less-useful. For example, if fast walking speed is due to a healthy cardiovascular system, and you notice that your walking speed is low, you might train your walking speed. With effort you might get your walking speed up to 'very fast for non-athletes'. But if you had poor CV health for some underlying reason, you wouldn't have addressed that reason, you would just have masked the proxy. Of course, training walking speed is likely to have positive effects on your CV health, so I'm not saying "don't bother walking faster", I'm just saying that it may cause it to be a much more flawed indicator.
What we need, in order to understand these proxies, is an understanding of the mechanism by which they work. Take this example: Suppose I am a smoker. I notice that I walk very slowly because I have bad cardio vascular health. I hear in the paper that walking slowing is a marker for death. So I train walking fast. I get up to 'elite non-athlete'. Even though I'm still smoking. In this case, even though I've successfully improved my health, as an indicator, my walking speed will over-predict my health.
For grip strength it's even easier, since it seems very unlikely that actually have a strong grip is realistically correlated with anything health related. Rather, have significant untrained strength is probably very well correlated with a host of genetic, enviromental, and hormonal factors that would likely be strong predictors of health.