SMTP and lost password link

I have created a similar topic under the Theme My Login (TML) plugin regarding this problem but having spent a lot more time doing further testing I now believe the problem is with WordPress itself!
I have the WP-Mail-SMTP plugin installed and it is set to send mail via my hosting company SMTP server – and it is working fine. However if I test the lost password link on the WordPress login form no email is received. If I switch WP-Mail-SMTP to send using the PHP mail() function then everything works fine (including other auto generated emails like add new user).
It would seem that auto generated emails from WordPress can only be sent using the PHP mail() function. The consequence of this is because the email is effectively coming from an unknown sender (i.e. the website) some service providers will either block or mark the email as SPAM. Is there any way round this problem? Regards