If Hogwarts has a book and quill that identify children with magical potential, why was Delphini able to avoid detection?

Question

According to Pottermore, there is The Quill of Acceptance and the Book of Admittance, which together identify all children who exhibit signs of magical potential. According to the article

The Quill's sensitivity, coupled with the Book's implacability, have never yet made a mistake.

If so, why was Delphini not identified? Tampering seems unlikely since the book

has not been touched by human hands since the four founders placed it there on completion of the castle [Hogwarts].

Wouldn't that have meant her name would appear and she would be sent a letter to Hogwarts, thus everyone would know about her?

Answer 1

We don't know whether her name showed up in the books as

Delphini Riddle (which would have been monumentally surprising), Delphini Lestrange (merely moderately surprising) or Delphini Rowle (not surprising at all)

Obviously when the name appeared, Voldemort's placeman was in control of the school so he may simply have removed her name (e.g. her true name) from the rolls.

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Even if her name did show up in the Book of Admittance, her adopted mother could have gotten out of sending her by simply telling the school, when she reached the age of 11, that she was too ill to attend or that she intended to home-school her.

SCORPIUS: You’ve never been to Hogwarts?

DELPHI: I was — unwell — as a child — for a few years. Other people got to go — I did not.

SCORPIUS: You were too — ill? I’m sorry, I didn’t know that.

DELPHI: I don’t advertise the fact — I prefer not to be seen as a tragic case, you know?

Regardless of her lack of formal education, she was evidently well schooled in the dark arts.

Answer 2

The Quill detects potential students when they exhibit magical abilities, not when they are born, meaning that she wouldn't have been detected at birth, but more probably several years later.

Assuming that the Quill is magical enough to write up an useful name for the school to find the student, then rather than her birth name, the Quill might have recorded her adoptive name (Rowle).

Afterwards, her adoptive mother actually claiming she was ill is perfectly credible, and no one at Hogwarts would've questioned it.

Answer 3

If she was Delphini Riddle people probably wouldn't have noticed the surname. Remember, many people didn't know that Tom Riddle and Lord Voldemort were one in the same person. Also I was thinking, who's to say she was born and raised in the UK. The book of admittance and quill of acceptance surely only pick up magical children born and living in The United Kingdom, not the whole world. So perhaps Delphini was born out of the country? (not a hard feat for Voldemort to get Bellatrix to leave for a little while) and then raised outside of the country until she was past the age where she'd receive a Hogwarts letter?

I do like the theories that she was raised under a different surname though. I think that is quite credible.