I listened to this also about a hundred times. At first it sounded more like an "R" to me, but then I listened to it more I totally get what you're saying about it sounding like an "H". I think what you're hearing is him kind of pushing air out as he goes to articulate the consonant. With a uvular consonant like this, it can also sound less distinct when native speakers of languages with such sounds articulate it more and more like an approximant (i.e. minimizing direct contact with the place of articulation).
Although it sounds kind of like an "H" sound when at the beginning of the word, you can notice that there is a clear uvular influence on the vowel coming directly after this consonant which lets us know that he did articulate an "R" sound as opposed to an "H" sound. I don't know anything about Hebrew though, that's just my two cents :P.
I believe the "r" sound in spoken Hebrew is similar to that in German, guttural, proceeding from the throat. At first, I struggled with the German "r" sound in exactly the way your area struggling with the Hebrew "r" sound, and though I just begun learning Hebrew, I almost immediately identified the "r" sound as analogous to the German counterpart. Perhaps a native speaker will correct or support my assertion here.
If I understand it correctly, normally in the word רואים the second syllable is stressed. However, in this case it seems that the first one is stressed a little bit more. Is it just me, or that "לא" somehow changes the pronunciation of the word? If so, what is the rule regarding this?
(Native Hebrewer) didn't notice it so far, but I think you're right. If I listen to myself saying this sentence, the לא steals the whole stress from רואים, so it sounds like one three-syllable word "lo-ro-im" with a stress on the first. In a stand alone גברים לא רואים the last syllable would get it's due stress; I imagine here it's different because of the structure of this sentence. Because of the contrast to the first part, the לא is crucial, the רואים is almost redundant.