Let's not conflate two different problems with BMI here. One the one hand you can have a low body fat percentage and still have a high BMI, but that only applies to body builders who exercise at a near professional level. Such a person will not get wrongly diagnosed by his or her doctor of being overweight. So, this shouldn't be a problem, however, as Carey Gregory points out, some insurance companies in the US make decisions about coverage and premiums purely based on BMI, which can lead to unjust decisions. A more practical problem with BMI is that it will underestimate the risk of cardiovascular problems and diabetes in people of certain ethnicities, particularly Asians. As recommended by the WHO, Asians should keep their BMI below 23 kg/m^2.
Then having cleared up these two real issues with the BMI, let's consider the context in which the argument for a fat tax and the denial of medical services are made in the sources quoted by the OP. The medical problem that at hand is that health problems caused by a poor diet combined with lack of exercise account for the lion's share of health care costs. The US is a special case where 50% of the health care costs is due to an inefficient system, in most other Western countries, the burden of health care costs to society is about 10% of GDP. But even that 10% of GDP is mostly due to people eating too much fat, salt and sugar and not doing enough exercise.
The people who choose to eat too many Big Macs are not only making me pay for my health care, they are actually limiting my health care options. The health care industry is hard at work at fixing the bodies of people who through their own faults, have wrecked their bodies, therefore I don't have to count on being treated in an optimal way. If at age 90 I would need a new kidney, I will be rejected because of my age despite having the fitness of a 60 year old by that time.
There are also costs for society outside of health care. Your car is significantly more expensive because the workers at the factories where cars are made are not making the right lifestyle choices. If you buy a plane ticket, you're paying more because transporting heavier people requires more fuel, the costs are shared by all passengers; people only pay for their extra checked luggage above their allowance, not your checked fat. This has led to calls for the system to be modified. The fat tax mentioned here is a fee that overweight people would have to pay. Contrast that with the notion of a "fat tax" in the source quoted by the OP. There it's about imposing a VAT on fat, which is a reasonable way to get the population to stick to a healthier lifestyle, thereby drastically reducing the costs incurred on society.
In conclusion, while it may look like the BMIs of very muscular athletic people poses a problem with using the BMI, a closer examination of the relevant facts reveals that this is not a major problem. Rather, it are obese people whose BMIs do actually reflect their miserable physical state (and also people with a normal weight who eat an unhealthy diet) who are making everyone pay a hefty fat tax, and they are making the quality of the health care available for you a lot worse. Bureaucratic problems with athletic people having high BMIs are trivial to fix, unfair as such problems may look like, let's not forget that at age 80 you are not eligible for a heart transplant, no matter how well your medical prognosis is. How unfair is that?