How exactly are you trying to print those PDF files to the HP printers? From Adobe Reader? From Adobe Acrobat? Or are you just somehow sending them to the printer itself?
Typical HP and other desktop printers either don't directly support PDF printing or only support subsets of PDF.
Assuming you haven't tried this already, try printing the PDF to your printer from either Adobe Acrobat or Adobe Reader.
Yes, from Adobe Reader. I've just installed Adobe Acrobat XI in my laptop and I will try to print using Adobe Acrobat on Tuesday when I get back to work. I think our Marketing manager also tried to print directly from ID with no success but I haven't. I will try to print directly from ID too to see if that solves the problem.
I was able to try this today. Typical PDF printing would be using Adobe Reader and this fails. I tried printing with Adobe Acrobat and it also fails. Printing directly from ID worked though.
Any other suggestions on how to fix the issue with the exported PDFs?
Ask in the Acrobat forum. You'll probably get way more help there.