That's how hairNfur works unfortunatelly. You can see it by yourself: go to H&F modifier's last rollout display and turn on display as geometry option. Now hair will be displayed as geometry in viewport, that is exactly how Corona renders it. See how you can't make tips to be zero sized no matter what.
There is one trick you can try however. Make tips transparent through material and that should give much nicer look. Plug gradient ramp into opacity slot and under coordinates rollout choose WU radio option, set first and third flags to white colour and second flag to black. Slide 3rd flag to right at about 80-95% position and you should be good to go. Notice however, that this can significantly increase render time, so use it with caution.
