You need to do more pragmatic basic phone calls than relying on an irrational rumor, which you unfortunately believe is legitimate. Simply pick up the phone and start calling and you will be quickly, and politely, properly educated.
The price for liability insurance, workmen's compensation insurance, as well as labor are expensive and the price of firewood is NOTHING in comparison.
You want a tree company that is fully insured, otherwise the possible bad out comes are numerous and gravely serious.
What you are asking has nothing to do with the reality of the seriousness of taking down a tree - it costs money for legitimate reasons.
The price of selling firewood next year - the time for seasoning of the wood - compared with the extensive labor of removing your tree - the literal physical labor and hourly wage (and insurance coverage); let alone chopping, splitting and storing of a partial portion of the wood from your removed tree is not comparable to what you are asking - To put it mildly.
What are you referring to when you say "I'm not even so much interested in getting paid for it." ? You are not selling anything. You are looking to hire someone to do dangerous, labor expensive and insurance expensive work to take down a 120 foot tree.
Further, in your last sentence, if it is damaging your house, the closer it is to your house, fences and such, understandably make the job more labor intensive, and imposes more liability.
Best of success in pragmatically educating yourself by phone conversations with tree companies.
