A WebContent filter would have nothing to do with Safari having the option to use private navigation. However, keep in mind, your navigation is only private locally on the device. Any network utilities can still see all network traffic from the device on the network level. A WebContent also would not prevent someone's ability to clear browser history.

You may want to check to see if you have a configuration profile targeting Safari, as private browsing availability and someone's ability to clear history would be controlled by a Safari Configuration Profile. 

If you're talking about the Restriction profile 'Web Content Filter' and using the 'Automatic Filtering' it does turn off the Private Browsing option in Safari as well as the ability to delete browsing history. I tested ours just to verify it was still working and it does still show they are still blocking the Private Browsing option on our Student devices that the profile is applied to. I've dropped a screen shot of my settings for you to compare. We do use a filtering appliance for student filtering. 

Hi,

I've the same parameters in web content filter ("Automatic Filtering").

The Private Browsing is enable but the possibility to delete browsing history is disable.

Interesting. It really doesn't make sense that yours doesn't function the same as mine. I wonder if there's another setting that might be interfering with this. Might be something that Help desk can figure out with you.

Sorry I couldn't help more.