The Greek ρ sound isn't the same as the English r sound. I think it is closer to the l sound, perhaps somewhere in between. Also I think Greek letters don't blend together in the same ways as English-speakers are used to.
Therefore, -ατρο- sounds more like -atero- than -atro-.
(Don't quote me on this, this is just my understanding of the sounds!)
While you're right that the Greek ρ isn't the same as the English r sound, it has nothing to do with l. The Greek ρ is like the Spanish single r, but you may hear a rolled r occasionally with over-enunciation. As for the recording, it's not great: there is indeed a gap between τ and ρ, where there shouldn't be one. Try listening the phrase here, it's very clear.