And as an Spanish speaker, I've found that, oddly, Greek people "sound" exactly like Spaniards. In the sense that you would swear they are Spanish and yet you don't understand a word, it's uncanny! Is it the same for you guys, the other way around?
Yep, nobody in Spain ever believes that I can't really speak good Spanish, because I sound like a native. I had a friend pronounce Greek words transliterated to Spanish, and he sounded like a native as well.
There are a few minute differences, like the "s" sound being a bit farther forward in Spanish, or the "rr" in Spanish being rolled twice (in Greek it's only rolled once), or Greek having a "z" sound (which Castillan accents don't have), but largely it's more or less identical.
And extreme syllable-timed language family (opposite of these) are languages Tagalog, Malay, Indonesian. EVERY syllable is pronounced and it becomes a mouthful but there's a strict cadence that comes from it. Foreign words break it a bit but native words are "ma-ka-ba-la-bu-sa-ng-ah-ga-ta-na..."
In the same way, Brazilian Portuguese sounds eerily like a made-up language pronounced in Russian, for a Russian ear. Many Indo-European languages are very similar phonetically, despite being completely different in every other way.