When you "Print to PDF" a web page, the first responsibility lies with your browser to create the print job.
And in this case they have to create a PostScript file for the job. (Only the next stage, when the virtual "PDF printer" comes into play, creates the PDF from this PostScript input. Unlike LibreOffice, OpenOffice and MS Office, browsers are not [yet] able to directly "Export to PDF". Update: Apparently, Chrome does: as yms explains in a comment: open print dialog, use printer selection dropdown list to choose "Save as PDF". However, I found that by default it does not print backgrounds.)
Now you must consider two things:
Most browsers do have settings, which allow for "print images"/"don't print images" and "print background colors"/"don't print background colors" and some such.
So you should first ask yourself:
If no, it's not the PDF printer's fault.
As for the transparency features: PostScript does not support transparency (only PDF does). Therefor transparent areas need to be "flattened" for PostScript output (that is, transformed into bitmap images which try to mimic the look of transparent objects).
However, not all applications and browsers are doing a good job when it comes to this "flattening".
As long as you need to "Print to PDF", there is no chance in hell to get real transparency into the PDF file (you'll only get the 'mimikry' bitmaps).
Transparency here will only start to happen, once browsers start to be able to "Export to PDF". Or you may find a third-party tool, which can directly convert from HTML to PDF (without using the print intermediate step that converts to a printable PostScript first).