I don't know the ins and outs of her specific project, but what I presume is that she gets to hear a bunch of demos which were selected by A&R and then picks what appeals to her emotionally. When the record gets done, it is presented to the label and they give it a go or not (see beyonce documentary of I am sasha fierce or its succesor I believe). If they don't give it a go, they might force certain songs on you or the album won't get released. This also happened with Ed Sheeran on the album with Shape of You. If there was no record label involved, shape of you wouldn't have been on the album - and probably wouldn't even exist as we know it now - but the record label insisted on a rhythmic song like that one or else the album would be too dry. This is documented in the documentary on that album.
But these are established artists. I don't think any recording artist with the same status as Britney Spears had in 1999 has more than limited influence on the songs on the album if they are marketed big time by the label.
How do record labels check if something is ready for release? Do they want every song to be good? No, there are singles and there are fillers. Fillers are unimportant songs and as far as the quality is medium and it falls within the concept of the whole, it is likely to be acceptable for release. They can let rihanna work on a song here and there but they won't end up being the singles cause of lack of quality (i mean, most artists are not max martin, steve mac, mutt lange or greg kurstin). Depending on how many singles the label likes to release (nowadays it's mostly 2 singles, back in the days 5 was more common), they check if there are songs that can deliver as a single. If there are enough songs with that potential + acceptable fillers, you are ready for release.
When listening to new music I barely listen to fillers - often i despise them - but just focus on the singles. There is much more to learn in listening to singles which are picked by a bunch office guys who believe that these songs have a chance of climbing the charts.