One cannot copyright short phrases, which includes things like quotes, slogans, and individual lines from poems or songs. While most publishing houses insist on getting permission for everything, this is typically going above and beyond the legal requirements for the sake of risk management. It’s a sensible strategy: fair use provides a defense against judgment, not an immunity from prosecution. Moreover, it is an affirmative defense (that is, the defendant bears the burden of proof). Given how few theories regarding intellectual property law have actually been tested in court, then, many espouse a “better safe than sorry” approach.
Song lyrics are a place where “better safe than sorry” tends to be adhered to quite stringently. This is because the RIAA, which has proven itself willing to sue at the drop of a hat, has long propounded the theory that even a single line of a song constitutes too much to use without permission. It should be noted that there is no case law to support this, and in fact one of the landmark cases concerning copyright blatantly contradicts it. If using a single line was enough to constitute a violation, then the Supreme Court should have found against 2 Live Crew in Campbell v. Acuff-Rose Music (1994). It found in the group’s favor, however, in part due to the transformative use made of the song they were accused of using illegally.
Copyright law involves more than use and permissions, however, and that is where many people get in trouble. Take this entry from the Etsy store linked to in the OP, which incorporates a line from the Eurythmics’ song “Sweet Dreams (Are Made of This).” There’s a strong argument to be made in favor of fair use for this product. Its purpose is clearly commercial, but it is of a much different nature than the original work, uses a very small—even if quite recognizable—portion thereof, and would likely cause no negative impact to the potential market or value of the song. One thing I noticed immediately, however, is that creator has failed to credit Annie Lennox and Dave Stewart. Attribution is a small element of intellectual property law, but a basic one. It is one reason why works may include a list of credits even if they didn’t need to and didn’t bother to acquire permissions.
My answer to the original question, then, is that the Etsy shop seems to contain products involved in copyright infringement, but not for the reasons one might have suspected. Whether or not something crafted along similar lines would be considered a violation depends on how much of the song is quoted, whether or not attribution is given, and the unpredictable whim of the courts.
Standard disclaimer: I am not a lawyer. The above is based on seminars I’ve taken on copyright law and discussions with colleagues who have studied and/or practiced copyright law. The information may be out of date or based on a misunderstanding. It is always advisable to speak to a practicing lawyer. The information contained in this post is not offered, and should not be construed, as legal advice.