Read the fine print too, a lot of these "mental health counseling services" have carve outs that stipulate that they can pass along data about your sessions to third parties (like your employer.) Most of them aren't health care professionals so health care law doesn't apply.
Everything HR does is for the benefit of the company. They do not do anything to genuinely help employees. You are a replaceable cog and the moment they decide you're not useful, you will be tossed out. Never trust them or the structures they put in place.
Good HR people see their employees as tools and they know that tools need special care to work properly. Yes, they only do it because it's best for the company.
I got lucky and two HR members in the four big companies I've worked for that were like that. I guess it isn't the norm.