I imagine this strategy works against them as I can't think or a single respectable engineer who would be willing to do this. It may work in their favor of recent college grads.. but certainly not seasoned engineers.
Yup, their logic is very hard to understand. What am I supposed to do, take a week of PTO? I'd think they want to find people who badly want to work at their company, but they are just not that kind of company yet.
I was thinking that maybe it would be kind of interesting and even possibly beneficial to work there for a short period before joining permanently. But could you do that in one week? I guess you could get a look at their tool chain, but you aren't going to learn much about what it's really like to work there in such a short period.