In Germany in 2006, 43,4% of people born in a certain year managed to make the necessary degree to be able go to a higher education system (universities, etc.). This is quite a difference to the 5-15% you assume to be "usual".
Additionally, the majority of universities here are public schools, with (recently introduced) fees of about 1000 Euros per year. This is also quite a difference to your assumption that 85% of students go to a private college.
Additionally, some traditional German qualifications ("Meisterprüfung", for example) are taught in other school forms, that are considered to be a university degree elsewhere.
Looking at the other European countries, the numbers are different, of course. That's party due to the fact that some countries require collage degrees for certain jobs not necessary elsewehere. In Sweden and Finland, for example, nurses seem to need one. In Finland, up to 71% of people born in a certain year seem to start a college education.
For other numbers, please see the fourth table here: http://tinyurl.com/dn22rh. The third column indicates how many percent of people born in a certain year start a higher degree. For example, it was 32% in Belgium according to the 2001 OECD study.