The reason why foreign residency programs aren't considered valid in the US is quality control, from both competency and medico-legal standpoints. If you were CEO of a private practice or hospital in New York City, who would you hire? A grad straight out of a US residency or one out of Swedish residency? The safer bet is the one straight out of US residency for numerous reasons: you can more easily trust and call his references, he has already likely taken the US medical licensing exams, you don't have to give him an English comprehension test, familiar with the mess that is US medical system, etc...
Doctors are people like you and I. They are imperfect and make mistakes. There are plenty of brilliant doctors out there and not-so-good doctors out there. It takes responsibility on the patients' part to advocate for themselves, do some research, and find the right fit for them.
Make sure your physician is evaluating and treating your Lyme. Lyme is relatively uncommon in the Southeast US compared to the Northeast US so physicians here are not as experienced in treating it.
I would also seek a second opinion from a neurologist if you have not already. If you feel that you have cognitive impairment now, then the neurologist may feel that a brain MRI is indicated. This may not affect management, but may provide you with prognostic information.
While having a good memory is important for cognition, it is just as important to be able to forget memories. There are probably limits to how efficiently our brains can scan memories for information relevant to a given situation and having more memories decreases the efficiency of this process. Also, when you can find almost all knowledge about anything on Google in just a heartbeat, it's inefficient to try to memorize most things. As Einstein said, "Never memorize what you can look up in books."
It's not an uncommon strategy for clinicians to use questions like that to get parents or patients, who are dealing with an inordinate amount of stress, to let down their defenses with the intention of directing them to self-assess their resolve. The author may be able to take care of her child now, but how about when he's 18 years old, when his outbursts may start to hurt others. There are some families who are capable of overcoming the challenges of raising a developmentally disabled child to adulthood (such as this family) and there are some who can't. I've had patients break down and cry when asked pointedly challenging questions like this, however ultimately, this can be a helpful process for the parties involved when applied correctly.
I suspect that the author and others here have missed the true, veiled purpose behind the question, however that does not detract from the overall aims of her article or the clinician. In the end, the clinician's prodding has led to a led to a deeper raison d'être for both the author and the reader.