That's the video that popularized "cursive speech": https://youtu.be/blLJ5UIu3r8
For example: "buongiorno amico, come stai?" would be something like "buoongioOrniio aamiIicooi, comiee staAiee?"
It is basically adding random vowels around, stretching them and using a childish voice.
Of course, she wasn't wrong!
I think it is easier for you because all that stretching gives you the time to focus more on the single words, also Italian speech is different from province to province. Sometimes it is also hard for us to understand other Italians, mostly because each region's native speakers mix some dialectal sayings and pronunciation into their version of Italian. We have tens of Italian languages in Italy, but the more you live here the more you understand other Italians beside your own (closer regions sound more similar but going from extreme north to extreme south it gets really different).
I believe this is what they call vocal fry.