I know that the sentence you can't out-train a bad diet has been used by a US native speaker (and parroted by a few others), but it's the only use of out-train on Google, and in fact it's a poor use of the prefix “out-”.
To outrun – to run faster than (predběhnout, předstihnout) (e.g. a hare can easily outrun a tortoise), to outspend – to spend more money than (e.g. the social security ministry usually outspends the transport ministry), to outrank – to have a higher rank than (a colonel outranks a captain), to outswim – to swim better/faster than (a seal can outswim most fish).
V daném případě jde však o zkomolení smyslu předpony “out”. Špatná strava netrénuje, necvičí. Člověk nemůže trénovat/cvičit líp než špatná strava.