What do you mean by that? There is no evidence that antibiotic-refractory Lyme arthritis is due to chronic borreliosis, but instead some other chronic consequence of the initial infection.
The spirochete may nevertheless be present even if symptoms arise via other mechanisms. I do not think "antibiotic refractory" and "chronic" are synonyms. You may be right about antibiotic refractory Lyme arthritis, but that does not negate the concept of chronic Lyme.
Spirochetes according to some studies do persist after nominally adequate antibiotic courses. Both "chronic" and "refractory" need proper definition.