I've checked this link but i'm afraid it didn't help my understanding in this example:
とし子ちゃんにきくと、やっぱり自分のことをふつうだと言った。
When she asked とし子, とし子 also said that her own affairs were ordinary (my, probably wrong, translation).
I don't understand the use of を in this sentence. There is no verb in the quoted sentence 自分のことをふつうだ which takes an object.
I came across a similar structure once AをBと思う (to regard A as B). I'm wondering if something similar is going on here? This leads me to the same understanding given in the link i.e 'call A like B'
Maybe "she spoke about here own affairs as though they were ordinary"? Am I getting closer here?