Yes, people have been charged if they determain it is customer abuse.
Frankly, I think it could come down to a decision by some individual at the refrub center. What you described could be looked at by Dish as something not worth charging you for (as in you being irate), but they will charge if it is a clear or egregious example of customer abuse. I think you should have just called and said that your HDMI came loose and left it at that, as they would have no reason from you that it was anything more than possibly loose/damaged when shipped, or Dish may believe that the kids or dog may have done it and Dish would just swallow it.
However, I can say that how Dish chooses to resolve a situation or how far they are willing to "look the other way" or make exceptions may involve the following factors:
1. Monthly bill: Is this a low-end sub who is gonna cost Dish money as the return on the low end packages are not as great? Or is this a fat cat who has never had such claim in the past. Believe me, even Charlie has said that customers who cost him money can leave and he it seemed he would hold the door open for you. He gave as an example, a low package customer ($30+ or the lower packages) who would call Dish for some of the most lame complaints or rants about not having certain channels, etc. Ergan said it costs him a dollar per minute when folks call toll-free, and at that rate, a low end customer was costing him money--no profit--and that ought to consider other providers. However, if a customer has malfunctioning equipment, problems with their system, legitimate concerns about their bill or would like to upgrade, than he said Dish would certainly do everything they could to make things right and get them on the latest technology if they wanted to upgrade and qualified.
1a. How long has one been a customer. Loyalty does count for something, but not everything.
2. Does the sub upgrade often. Meaning the individual continues to spend money on Dish, and with the subsidy from Dish, it does represent some return to the company.
3. Any previous disputes, even for a PPV.
4. Is this a DHPP customer. Now, even DHPP does not protect one from charges due to customer abuse, but Dish does feel you are already paying your way towards RMA's and will probably be more willing to give you the benefit of the doubt on "suspicious" damage.
Now, I'm not saying that the highest paying customer with no disputes is NOT going to be charged for damage that MAY not be clearly customer abuse, but Dish, more than any other MVPD I can think of, really does harbor suspicions of low-end subscribers from whom they don't make as much money and now are costing them. Now, someone who has a $200 per month bill--yes, they are out there--Dish is willing to eat some to a point because they can get that money back in no time and be back in the cream of $200 per month.
If this situation becomes a problem for you (being charged for the damage), please contact the Executive CSR's to see if they are willing to help you. Good luck.