Quite simply:
This has become such a prevalent excuse for missing work that it has come to be understood as not available. The book of Stobo Church, published in 1907, reveals how easily the word can be misinterpreted even in a context where its real definition is quite clear:
1770: Five times this year he was indisposed; and on four Sundays he preached elsewhere; nine in all marked no sermon. The Sacramental Fast was held.
The vicar called in sick, and the records show that, but a person who doesn't know the definition could easily construemisconstrue that he was "unavailable".
In Doors to Madame Marie, likewise:
You knew when a girl had her period because, as the French put it, she was "indisposed." It was a privilege to be indisposed; you could be excused from anything stressful. I kept dreaming of the day when I, too, could say that I was indisposed.
English permits pretense just as well as any language, and if we pretend long enough it becomes real to us. I rarely hear the expression used to mean "I'm sick," so my default interpretation is "I'm not available," unless the larger context indicates, "I'm sick."
Interestingly the etymology of indisposed would be quite friendly to unavailable:
c.1400, "unprepared;" early 15c., "not in order,"
from in- (1) "not" + disposed;
or else from Late Latin indispositus "without order, confused."
Mid-15c. as "diseased;" modern sense of "not very well" is from 1590s. A verb indispose is attested from 1650s but is perhaps a back-formation of this.
late 14c., from Old French disposer (13c.) "arrange, order, control, regulate" (influenced in form by poser "to place"),
from Latin disponere "put in order, arrange, distribute," from dis- "apart" (see dis-) + ponere "to put, place" (past participle positus; see position (n.)).
The conventional definition implies: parts of me are out of place. Shifting the frame of reference, the meaning becomes I myself am out of place.