A blogger in the USA refers to himself as "Trey" hence "Trey's Blog".
His entry there on anaemia includes the following:
CML drugs do a good job suppressing leukemic cells, but for most of us our blood cell counts can go too low, especially after a month or so on the drug. This may continue for years before leveling out. That causes many of us to live on the low end of normal or below normal for WBCs, RBCs, hemaglobin (HGB), hematocrit (HCT) and sometimes platelets (PLT). The result is a type of drug induced anemia and fatigue can result ... Many of us with CML have for the longer term what is called Anemia of Chronic Disease".
It does appear that CML patient on TKIs can be anaemic without having out of range iron, B12 or folate readings. This seems to be a likely explanation of CML fatigue.