This sentence is clearly wrong,and on multiple levels. First, as you said it would require shee. Second, it's shí and not shi, and is not required (if shee is added of course), except for emphasid. Thirdly, itʼs aniitsįʼ and not aniitsį́ʼ. Fourthly and most importantly, for inalienably possessed nouns, actual possessor marking is mandatory, so it should be: [Shí] shiniitsįʼ hólǫ́ (=me, there is my cheek).
That's very interesting and useful; thanks!
Does this last point then apply to anything starting with "Á" - the "Á" gets changed to the possessive?
For 99.9% of these words, yes. Note that it can be a- or á-. In the latter case, the high tone must be kept: álaʼ > shílaʼ (hand > my hand).
For a small number of words, a- is part of the actual word, so it doesnʼt delete. Comes to mind: ashkii (boy), atʼééd (girl), asdzáán (woman), ałtį́į́ʼ (a bow [the weapon]). For these words, possessive is in she- (i lowers to e because of proximity with the low vowel a): sheʼashkii, sheʼasdzáán (my wife), sheʼałtį́į́ʼ.