The marginal cost of a student is significant and non zero. It's a rival good because the professors time is finite. We're talking about university. Your "free education" offer via Wikipedia on the other hand is an example of a non rival good.
I can understand if you think it's a club good, I disagree, but regardless it's not a public good. You're still asking the entire populace to fund something which most directly benefits a select group. Which in the specific case of Argentina turns out to be a group of people who come from backgrounds of above average wealth. Which is what the lanacion column was about.
I never said it's a public good, I said it's not a private good - which is a difference. 100% purely non-rival goods rarely exist in practice, even Wikipedia is not an example as - to say use your examples - a server being able to handle 1000 users might not be sufficient to handle a 10 million users. Yet, if you have a server farm that can handle 10 million users, adding a single user more to the existing traffic doesn't make a significant difference. The same applies to universities.
Regarding whether higher-eduation should be private or tax-funded - that's a question society needs to decide. There are arguments for both options, and I personally prefer a system as it is in most countries in Europe, but if one chooses a system where students are required to pay tuition, I think it's not very smart to implement it in a way to charge only the students who are about to graduate, while the ones that study several years and drop out before the exam (and thus are producing similar cost as the successful students) get free tuition - that's basically an incentive for being unsuccessful in terms of finishing a university degree.