There is no governing body that dictates what is considered right or wrong usage of the English language. Much of the usage can be agree upon, but occasionally, there is disagreement.
That is the case here. Some say it's wrong; some say it's right. That's essentially what Swan is saying. Put another way, some of us could argue that those grammar books are wrong.
I checked a few dictionaries and they agreed on the usages of disinterested. Here's what Merriam-Webster has:
Definition of disinterested
1a : not having the mind or feelings engaged (see engaged sense 1) : not interested
// telling them in a disinterested voice
— Tom Wicker
// disinterested in women
— J. A. Brussel
b : no longer interested
// husband and wife become disinterested in each other
— T. I. Rubin
2 : free from selfish motive or interest (see interest entry 1 sense 1a) : unbiased
// a disinterested decision
// disinterested intellectual curiosity is the lifeblood of real civilization
— G. M. Trevelyan
Judging from the entries, we can safely say that disinterested meaning not interested has currency, and so I am disinterested in English would be understood. Again, as Swan advises, this would we accepted by some and rejected by others. If you want to be safe, stick to "uninterested" meaning "not interested", and "disinterested" meaning "not biased".
M-W has a nice little piece on the history of the two words, Is This Cat 'Uninterested' or 'Disinterested'?. It gives the following:
According to our citation files, disinterested is most commonly used to mean “not biased; free from selfish motives," while uninterested is commonly used to mean "not interested." Yet when these words entered the language, uninterested meant "not biased; free from selfish motives" and disinterested meant "not interested."