Why does the APA style call it 'the footnotes page' even though the notes are not placed at the bottom of pages? The APA style recommends the use of either footnotes or endnotes. 

The term 'endnotes' means notes are placed in a separate page in the back matter.

The term 'footnotes' means notes are placed at the bottom of relevant pages.

However, I have seen official sample APA papers with a page in the back matter entitled 'Footnotes.'

Why does the APA style call it 'the footnotes page' even though the notes are not placed at the bottom of pages?
The APA publication manual describes the way you should submit your manuscript, not the way the paper will ultimately be typeset. For APA journals, footnotes are grouped at the end in the manuscript but they appear at the bottom of the relevant page (actually at the bottom of the right column) in the final published version. Similarly, you would traditionally put tables and figures at the end of your manuscript, one-by-one on separate pages but once published in a journal, figures and tables will be embedded in the article.

If you are working on a student paper, you should first and foremost follow the instructions from your instructor but there is no reason to put footnotes at the end of the document. The APA publication manual provides useful guidance regarding language or statistical reporting but it's not a typography textbook. In fact, some publishers ask authors to follow (some) APA guidelines for the submission even if the final publication will have a different layout than APA journals.