Does subsidizing higher education increase or decrease signaling costs?

As of 2004, only 16.7% of the cost of Korean higher education was picked up by government, as opposed to an OECD average of about 77% (see this paper).  That’s a relatively low level of subsidy.  And yet Korea has one of the highest degree-granting rates in the world, the status of the school you go to is all-important, tiers of quality are fairly rigid, admission is closely linked to exam performance, and doubts have been raised about how much people actually learn in those schools.  At least when it comes to surface phenomena, it appears Korean higher education has a lot to do with signaling.

In Germany they just made the universities completely free, and in the past they were quite cheap, which of course means subsidized.  Germany also sends a relatively high percentage of its population to vocational training, where presumably the students learn some concrete skills.  Could it be there is too much slacking in German universities (which I have interacted with twice, both as student and as professor) for attendance to serve as a very effective signal?

Can it be the case that a government subsidy, by limiting privately-perceived quality and returns, can lower private signaling costs?  Should advocates of the signaling model therefore be more favorably inclined toward subsidies?