Not being hypothetical here, you are squatting and violating TM law. You will lose a UDRP. Take the $1,000.00 and run. If you push them enough, they may want to make an example of you.
What I find funny is you claiming they no right to their legal name and saying theu don't have rights to "group". All that means is they cannot claim "group" in itself as a TM, but they certainly do have the TM for "Health Finance Group".
1 - You don't need permission from court/WIPO, they could care less if you shoot yourself in the foot.
2- Companies can not show bad faith if you registered thier TMed domain. Your actions will show bad faith or not.
3- What they are doing is trying to be amicable about the situation. Be offering you a settlement, they are not acknowledging your rights to the name. It is aobut dollar and cents.
4- ugh, the rule of thimb is similar or confusingly similar.
5- ugh again.. so what they used an abbreviated version of thier name. In domains, the shorter name is better. But legally are listed as thier full name.
6- Take thier offer and run and hope you don't anger them by your ignorance.
Suggestion- Use the search box and lookup "trademark" and "TM", it will help you in the long run and save me writing my thesis of cybersquatting 101
EDIT TO ADD: I was writing my response when you posted again... You have the domain parked at SEDO, people do that to capture traffic, why register and park a domain unless you know there will be traffic?, additionally, offering the $20,000.00 is a sign of bad faith. Did you ever bother to Google or Yahoo the name in question to see if it was a TM? Or the USPTO?