Re: Yes, good idea
It's not that simple at all. Obviously mentioning in the same item both your employer and a controversial view relevant to your employer's business is potentially going to get you in trouble but I sincerely doubt this is what they're seeing.
Is it fair to say that if your employer is listed anywhere in the internet as HO you aren't allowed to publish anything political because a simple search will uncover your affiliation? That's more like how their internal email sounds to me.