Yes this issue happens when the WordPress installed on the site does not have any option to send mail. As the wordpress is written in PHP, the mail() function requires to be enabled from host end to send the mails. So any password recovery or mail to and from the server won't be possible. This applies to even the contact form that has the confirmation mail option.
So your best option is to either comment on that wordpress website on page or post. And then you can ask the owner to reset the password. If you're the owner of this blog then you have to go to your host. Login to the cpanel and reset the password from the mysql table where wordpress has the password entry. This works for many users and seems to be the only option that people have these days when such issue happens.
You may want to contact your host if you wish to enable the mail () function. Because that way the problem can be solved much quickly.