OK. The Kern in Sequoia Park gets a lot of traffic -- both hikers and stock. The trail crew camps there for weeks with about 10 head. In addition, there's a fair amount of private stock traffic through there. It also gets a pretty good amount of hiker traffic from the Hot Springs up. That's one area I'd be kind of cautious about just drinking the water out of the main river. Odds are, it's OK, but the risk is somewhat higher than other water sources. Also, there are definitely beaver there. Not completely sure of the history, but I think they were introduced in the 30s. There's no eveidence that they're any greater source of giardia in that part of the Sierra than any other mammal, but they do live in the water so any cysts they do carry would go directly in.
There's an unpublished paper that finds that something like 7% of horses in Yosemite carry giardia. The same research team also measure the amount of, ummmm, feces they left per mile of travel and, from that, derived the number of giardia cysts they shed. Although only 7%, it's a huge amount of giardia potentially reaching the rivers and streams. It's a little suspicious it hasn't been published. But, I have the raw data and it's public domain because it was done in a National Park. As soon as Nature Notes comes back up (down for a remodel), I'm hoping to publish that as an article.
Mike's correct on asymptomatic carriers. I've read several percentages, but something like 20% of the population carry giardia but have no symptoms. I'm less sure of "safest" place to drink. Dr. Bob Derlet thinks the top 3" or so of a lake is best because of the UV light hitting that. In the great scheme of things, giardiasis is pretty rare in either Yosemite or Sequoia Kings. Definite cases, but only a few per season. Mostly, it's cows and not washing your hands after taking a crap (or, I suppose, cow tipping).
E. Coli itself is not the problem, usually, but is an indicator of other pathogens that could be there as a result of feces in the water.