"diese Daten" can mean "these dates" or "this data". Either translation is fine.
So, not only is the plural accepted in the US, it is actually the correct usage.
While using it as a mass noun is becoming more accepted, but is still considered incorrect by style guides.
ETA: I stand corrected. It depends on the discipline/field it is for in the US and which style guide it uses.
The Guardian style guide makes a good point.
"data takes a singular verb (like agenda), though strictly a plural; no one ever uses "agendum" or "datum""
Keep in mind that the APA is the American Psychological Association, yet another scientific organization which is making guidelines regarding scientific papers. In that use, data is most certainly used as plural, but that is not the only way to use data in the US which also accepts it as a mass noun in non-scientific usage.
I agree, actually, with the Guardian's point. My instinct is to use it as a mass noun, but I come from a region with a strong dialect.
However, The Guardian Style Guide seems to be a British newspaper (though I now see it has other editions) and the APA is a style guide used by the publishing industry in the US. It is probably growing in acceptability in both countries (as well as other English speaking locations), but maybe more quickly in some than others.
In speech, both are accepted. If you are writing an academic paper, you probably still need to use the plural verb in the US or you will have problems if the prof is strict. It is possible to lose whole letter grades from subject verb disagreements.
Or they deliberately want to show us alternative uses for the same vocabulary word, even if it is not in the context of the main point of the lesson. I have seen this in Spanish lessons too (the word "fuera" comes to mind). I find it useful to know that the same word can have other meanings to be aware of. Keeps us on our toes!
When used as an adjective, "diese", which describes "Daten", means "this". Without the word "data" or "Daten", "diese" would be a pronoun and then could mean "these", "those" or "that" http://dict.leo.org/ende/index_en.html#/search=diesesearchLoc=1resultOrder=basicmultiwordShowSingle=on
As for data, science and technology use many Latin words and keep them intact as datum for singular and data for plural; however, other uses for the word data correspond with the mass noun information and it is used as a mass noun in English as well, which would then take a singular verb. Consider your audience. If you are publishing a paper for science or technology, then you must use data as plural, as indeed these items of information can be backed as facts. Not all data is collected in the same painstaking way that scientists use and, in that case, I consider it to be general information and use it as a mass noun.