Preview won't display diagram in PDF
The PDF file format contains are series of code-like instructions that have to be interpreted and then rendered into a displayed image, and there are different 'engines' that do this in a variety of ways. Apple's own CoreGraphics engine works differently from Adobe's. Of course, both contain a number of bugs! 

It's also possible that the PDF was not created 'to spec', and different engines are more or less forgiving in how they deal with syntax errors.

You could try Exporting it from Preview as a PDF, which will 'rinse' the PDF data through CoreGraphics, and which might fix the problem. Or it might do nothing; or it might hide the diagram when viewed in any reader.

PDF Reader Pro Lite is likely to use Apple's native APIs for creating windows with a PDF view.