Please!?! OP has presumably run off screaming wishing his original question, which hasn't really even been answered by consensus, had never been put.
Quoting Mynors "It should not be forgotten tha tthe owner of the tree owns overhanging branches, both before and after they have been severed from the remainder... Once a branch has been severed, therefore, it should be offered back to its owner, and only disposed of with the owner's consent."
It seems clear enough to me that since it is not an offence to allow a branch to encroach (many many people tolerate and even enjoy this sort of encroachment), the owner may be content too to own a living branch but not wish to own a dead one, hence the duty of the abater to offer and then only dispose with the owner's consent. The branches may still belong to the tree owner, but he would not be faced with disposal costs if the branches had been left to grow. Since encroachment is tolerated more often than not as an ordinary, natural facet of life, it is on balance fair that the abater should dispose if allowed to by the owner.
The arborist is just the agent of the abater. His duties to chip, dump, transport etc are a secondary issue. Let's not get the two mixed up. Also it is I find very wise not to mix up everyday pragmatics like resolving disputes amicably with the legal position if it all goes horribly wrong. If it goes wrong the law will decide who is right based on the assumption of two hypothetical reasonable people.
It follows that if a pragmatic non-confrontational person wants some light into their garden the arborist should be able to advise them of their rights and then exercise a different skill by suggesting or brokering a compromise solution. A few people on Arbtalk are making the mistake of assuming that because most situations are resolved without a fight on the day that the law is too strict, too old or just wrong. It's not. It's there as a fallback and a framework for reasonable behaviour and compromise.
As I said about 10 pages back, this subject never gets resolved. Not for want of the clear and settled correct answers being readily available but because of confusion and possibly more than a little stubbornness amongst individuals who are prepared to state that they know the law better than the law does. It does our industry and our customers no favours.