Acrobat and Illustraor Show Different Content

Hello,

I have received a PDF file to work with its text, which was exported from Illustrator. The issue is when I open it in Illustrator (several versions), I see a different artboard:

In Illustrator, there are only three layers, and nothing similar to the Acrobat's vision of the document (or of any other PDF viewer): 

I cannot work in Acrobat Pro, because text is saved as image and is too bold to understand the letters:

Though the guy says, that other editors had no problem with it. Here are the examples of part of PDF and the same part in their document after work:

According to the data of their file, it was saved via CorelDraw. But if CorelDraw opens it correctly, Illustrator should also somehow open it. Perhaps, without the option to edit text, but without bold lines as well.