SDP - A user with full access to Assets can't add a new product - the link to add new product is hidden.

Hi,
We hired a new guy who will manage our company's assets. We have created a technician group Asset Administrator and assigned full asset permissions to that technician.
We have discovered, that going to Quick Actions - Asset brings the screen where a new asset can be added? but the Add New link near a Product Name field is not shown.

We tried this both on IE and FF - no luck.
The link is there only for SDAdmin group, but we don't want to provide the new tech with full access to everything.

Could you please let me know if there's a workaround for this issue?

Thank you,

Miron Shabalin