It is often explained, that the rule of thumb for exercising American options is to check when the benefit from the interest rate (sell the stock earlier, get the cash, put in the bank) is higher than the time value of the option. This is all clear in the positive interest rate environment, but the question is then - would we exercise some put options in case $r = 0$, and why would we do that? I thought, that there's no reason for such exercise, however according to [this paper](http://economia.unipr.it/DOCENTI/DEDONNO/docs/files/battauz-dedonno-sbuelz-real_options_and_american_derivatives_MS.pdf) it is even sometimes optimal to early exercise American puts when $r<0$. What am I missing?