[Animal]

Perhaps I missed it, but is Rachel and your other friends at work considered your subordinates?
If so, then as much as your going to hate me for saying this, I completely agree with your HR rep. It could be quite easily interpreted as favouritism on your part.
If that isn't the case and you are just co-workers then I personally see nothing wrong with socialling with them as long as your respective spouses don't. A couple of words of caution however, sexual harrasment. Be careful what you say and to who you say it. In 99% of all cases, and this is not be sexist, women hold the upper hand in hostile workplace cases.
As for taking it to the top, I don't know if I would do that. Often times, you end up making the situation worse and upsetting your immediate supervisor, which spells trouble and the end of your career.
Bottom line: If you are co-workers then just socialize away from the office, it's much safer for everyone involved. No corporation can dictate what you do on your private time, but I'd probably avoid the lunches and water cooler chats. If these people are under your direct supervision then socializing with them is not an option, business and pleasure don't mix.