Jesus Christ. The argument has been tedious from the beginning. The EFF statement is correct and accurate. Your refusal to understand why is what is tedious.
The Fourth Amendment says that no person shall be subjected to unreasonable search or seizure without a warrant. This is analyzed in three stages, as the Quon opinion sets forth in order based on the historical evolution of doctrine in this area.
The first question was, when has there been a search? The Court answered this question. The standard for whether a search or seizure has occurred is based on whether the person enjoys a reasonable expectation of privacy in the relevant material. This is the only standard, and it does not matter who is doing the searching; your boyfriend, your private sector employer, or a government entity, either law enforcement or a government employer.
[This is the "Fourth Amendment right to privacy"--it does not actually exist in the text. It is solely a creation of caselaw, and it is the basis of all American privacy actions. If you have no REOP, you have no cause of action at tort, at common law, or under the Fourth Amendment because the material is considered non-private. The REOP standard developed by necessity as the earliest part of Fourth Amendment jurisprudence, and it is used as the basis for all privacy violations in the United States, committed by all actors under all laws. When a private-actor privacy case comes before a court, as you have discovered for yourself, the first question is, "is there a REOP?" The court looks to the applicable Fourth Amendment cases to answer that (again, as you have seen), since that is the provenance of the standard. The reason for starting here is obvious: if you do not have a privacy expectation at the broadest measure, you cannot have one on a narrower field. Thus, if there is no REOP, the case is dismissed outright, because the material in question was not "private". If there is a REOP, the case proceeds to the particular restrictions applicable to that actor on the narrower grounds applicable under statutory or common law rules.
It is the REOP finding the EFF in part celebrates, because it strongly suggests that the Court believes that privacy interest exists in text messages, and a REOP finding applies to everyone, everywhere as the most fundamental dividing line that exists.]
Having established what is public and what is a search into private affairs, the next question was, assuming a search has occurred, who needs a warrant to conduct a search? The Fourth Amendment restricts the actions of the federal government. The Fourteenth Amendment, along with several key SCOTUS decisions on incorporation, extends that restriction to state and local governments. This is where the textual restrictions of the amendment come into play. Private parties cannot be sued under the Fourth Amendment, because the warrant requirement does not apply to them; the cause of action in such cases lies in tort or in statutory provisions.
In Quon, because the party conducting the search was a government entity, and because the Court assumed a REOP existed, the Fourth Amendment is triggered. The city needed a warrant. It didn't have one; the search therefore is presumably unconstitutional. This is the second part the EFF is celebrating, because it places a burden on government agencies to defend their actions, and creates a default presumption that a warrantless search is unlawful. The full set of Fourth Amendment protections apply.
But wait! The amendment protects against unreasonable searches, not all searches. Hench, the third question, what is an unreasonable search? The answer of course is spelled out in the numerous warrant exceptions, including the workplace exception argued by the city.
Here, because the service was paid for by the city, and because the purpose of the search was narrowly tailored to a legitimate purpose (budgetary assessment regarding overage charges on the accounts), the workplace exception applied and the search was reasonable under the circumstances. Thus, despite the REOP and the Fourth Amendment textual restrictions on the city's actions, the city was entitled to do as it did. Quon enjoyed the full scope of Fourth Amendment protections, which means the search must comply with the Fourth Amendment to be lawful. The search complied with the Fourth Amendment.
Thus, the EFF is happy that the explicit assumption provides Fourth Amendment protections (which, because of the REOP findings, spill over to all other cases) and Quon still loses.