I think there is a difference between accessing treatment and refusing it. It's only a very small point in the argument, and I don't think it affects the rights and wrongs about assisted dying, rather it's a point about the arguments.
Sure, there is definitely a difference between accessing treatment and refusing it - for a competent person the latter is an absolute right, the former is a limited right, limited by the law and the treatment being one of an accepted set of options for the individual's clinical condition. If assisted dying were made legal it would be added to the range of other options (which currently may include further active disease treatment and palliative care) for a competent adult with a terminal illness and less than 6 months life prognosis.
But for a person with those features I don't see why it should be, or would be, any less limited as an option and a right compared to the other options. I don't think you would be expected to, or should be expected to, demonstrate that you have exhausted other options, just as someone currently doesn't need to demonstrate that they have exhausted active disease treatment options before being able to access palliative care. If a competent individual determines that they do not wish to continue to pursue active disease treatment for whatever reason then their decision is respected. That should be the case too for assisted dying. Within the limits of the law (competent adult with a terminal illness and less than 6 months life prognosis) then they should be able to choose not to continue active disease treatment and/or palliative care and should be able to consent to assisted dying and have their decision respected.
Another point - my understanding from other jurisdictions, e.g. Oregon, is that we aren't in the world of palliative vs assisted dying as an either/or choice. Rather most people will move through each stage - so those that ultimately opt for assisted dying will have spent months on palliative case before finally opting for assisted dying when the palliative care no longer works for them. There is often a focus on pain, but actually autonomy, being able to make decisions for yourself and being able to have some kind of quality of life I think are just as important. The challenge for palliative care (even the very best, and I've seen it) is that it trades off pain relief for loss of decision making and autonomy as the person becomes increasingly more sedated.
Certainly, from my perspective, and from watching both my parents and in-laws die I can understand how individuals may not wish to go through that very last stage, which often seems to be hugely distressing for the individual, but without any way in which their distress can be meaningfully managed. But that stage is often perhaps just a few days, maybe a week. So it may well be the case that assisted dying is commonly used in the last few days as a choice to remove that horrible end stage (it certainly seemed horrible for both my parents, who were being cared for in an award-winning palliative care setting), rather than in the last few months.