We have insurance to cover our product and public liability. This policy covers our business and brand as a whole. When sending private label products, you will send stock out in your own brand and under your company representation. If you had an incident and looked to pass liability up the chain to us, we would be covered.
However, you have to consider that insurance companies will not pay out lightly, and our policy would most likely try to return liability to you. Therefore, we would advise you to speak to a broker and establish your requirements.
We have been operating since 2006 and have never had a claim against us. However, it is still prudent to know what your liability is and ensure you have the correct cover.