That study is highly questionable, mainly because it suffers from clear gender bias. A proper study would have had cross-references with different genders and sexualities (female tears on straight women, straight/bi men, gay/bi women and gay men; male tears on straight/bi women, straight men, gay women and gay/bi men). The study as is presents more questions than it actually answers. What is the alleged pheromone or chemical those tears have? Nobody thought to run a simple HPLC on the tears? If they had enough to significantly wet a piece of paper (several, in fact), it's ridiculous that you couldn't spare a few microlitres for HPLC, spectrophotometry, spectrometry, gaseous chromatography or anything that actually lets you figure out what chemical is causing what effect (and in the event that tears contain several unknown components, then you repeat the test with a pure sample of each unknown chemical and see which one gives you the same reactions on the test subjects).
Furthermore, the study leaves unanswered whether this is a gender-specific mechanism (i.e., if only women have it), a sexuality-specific mechanism (i.e., if only those who are sexually attracted to the gender of the crying person find their arousal diminished), or if it's a species-wide mechanism (i.e., everyone, regardless of gender or sexuality, will find their arousal reduced when they encounter the tears of any other human being).
And finally, there's the most gaping, ridiculously ignored fact: the effect a pheromone or volatile olfactory chemical substance has is extremely limited. We have pheromones in our hair and skin and their ranges have been repeatedly confirmed: you have to be very close in order to feel the effects. If the effect tears have is biological, then it should only work within a certain range, which is empirically not the case. There is a psychological (or sociological) component to the whole issue and trying to be simplistic/reductionist and blame it all on biology lets us wash our hands of psychosociological responsibility.
That is the worst kind of science: the sensationalist kind. I'm pretty sure everyone already knew what the study was going to turn up and they simply went through the motions to publish something sensationalist. Ugh. I wouldn't be surprised if they faked or rushed the whole thing and nobody bothered to fact-check or repeat it.