If you do not want to specify the type of studies you performed, it's going to be quite tricky, as Germans like to specify this very precisely - and that's apparently your challenge here.
If you want to talk about "studying abroad" in the general sense, I would go with the approach the website recommended. However, I do not agree with your citation "studieren ins Ausland.": "ins" is short for "in das" - and would mean that your studies themselves would go abroad, and not you as a person (for studying). I would prefer to use "studieren im Ausland" instead (which means more or less "studying while being abroad").
Although "studieren" here is being used as verb, it's trivial in German to make it a noun in this case. So, for instance, just by adding the corresponding article upfront you get to a sentence like:
Das Studieren im Ausland macht Spaß!
(which would be Studying abroad is fun!)
I also would accept this term "Studieren im Ausland" as a headline in a CV, as long as there is some more "beef" to it later on explaining what was actually done there.
However, in general, if you are in a CV situation, I would recommend to be as precise as possible: Just being there in Germany, for instance, is not considered to be "studieren". If somebody "studiert", then (s)he is either actively participating in a curriculum-based activity or in fact doing research on some topic. Moreover, the person needs to have some sort of "higher education" to be capable of "studieren". If the latter is not the case, you more likely would use the more neutral word "lernen" (translated literately: to learn) instead. So, "studieren" is always understood as some thorough and deep-minded activity.
However, unfortunately, "Lernen im Ausland" would be a laugh, as "lernen" would be too weak to justify going abroad...
On the other hand "Nach Deutschland reisen/fahren, um Deutsch zu lernen" is totally fine again (though you typically wouldn't write this in a CV either).