Both of these teachers are teaching for purposes of tajwid, or proper Qur'anic recitation. It's arguable whether that would be considered the source for "correct MSA." In terms of MSA, you have a few good answers here already, the gist being is that it's a tap, often realized as a trill. But the best would just be to listen to lots of people speaking. I think both in MSA and Classical Arabic, and even in the dialects, you'll find most speakers using something between the Spanish and leaning more towards the former. Some people definitely prolong it, though. Search YouTube for the football announcer Faris Awad (فارس عوض) for an example.
As to the second video, you should note that in tajwid, <ر> has two forms (referred to as "light" and "heavy") based on context which affect the realization of the consonant and the following vowel. In the video you posted, this is the heavy version. (And I agree his "heavy" ر is very distinct.) If you want to see the same person recite the light version - which is more clearly alveolar, check these two videos: 1,2.
In the tajwid tradition (and in the Arabic grammatical tradition) they always talk about takrir or takrar ("repetition") as one of the attributes of <ر>, but one "to be avoided." The apparent meaning here is that there should be some trilling/rolling, but not excessive (not sounding like more than one letter). Sometimes, you will find some teachers who emphasize the avoiding more than the including, which can lead them to avoid contact between the tongue and the top of the mouth altogether. But the place of articulation and other attributes of the letter as specified in the tradition make it clear that there should be contact and it should be a light trill. Maybe you will appreciate the diagrams and animation in this video. He illustrates some of the extremes as well as demonstrating what he thinks is correct. Around 2:20, you can see how he uses the fingers of his hand to demonstrate the front of the tongue with air escaping over the tip to make the trill.