I don't disagree with anything in your post. What you seem to be ignoring however is that this is not a situation that is in any way workable. In the first place this should be a negotiation between two parties, in Greece's case there should be a common interest for the union itself. To allow that to turn into the political pettiness of 27 different administrations is exactly why Greece's situation is completely unsolvable. Negotiations only work when both parties are acting in good faith.
It might have been political pettyness for some countries (Like Funky described above) but we cannot forget that the deal which was on the table when Tsipras became PM was proposed in good faith (Which for example in Germanys case had cost Merkel a lot of political power because the public wasn't exactly in favor of another greek package)but the greek goverment decided it wants something that was simply unachiveable (Kinda like May but who knows what her actual goal is in negotiations) if you consider these heads of states also have to get this through their parliaments (IIRC German public opinion was something like 75% kick greece out of the EZ during the high times).
I think May is falling into the exact same trap and is only playing for the home crowd while EU public opinion is turning on her (I think german numbers are something like 32% give them no concessions and 49% only very limited concessions) and at some point these heads of states can't ignore this anymore because unlike what Varoufakis claims they're still elected.
If you want to get maybe not so popular things done in the EU (And i think a lot of countries miss this point) you have to lobby for it all over the EU and not only play for the home crowd.