If you read a bunch of the reviews of all the 560 Ti cards on newegg, you'll quickly notice that a bunch of peeps are talking about how it sounds like a Jet Engine when it's at load.... Not something I'm really looking forward. If I'm spending this much cache on a vid card, then I'm not really thinking about hearing any Jet Engines. I had to live with that from the Xbox 360 for the last 6 years. (never got a slim)
Keep in mind, that sound would only occur for a few seconds. That said, most the time cards do this, it only happens when you first install the card, and stops doing that after it's been fully installed and drivers loaded.
I got this one http://www.newegg.com/Product/Product.aspx?Item=N82E168... (ASUS ENGTX560 TI DCII/2DI/1GD5).
With my case on the floor, I'm not sure I've ever heard the video card get above a quiet whirring, and I only notice if I'm really trying to hear it. I think they put a different number of blades on each fan to avoid a harmonic whine between them; if so it certainly worked.
If it can ingest a small cat or wild bird without doing damage to the fan(s) then you got a jet engine.
Avoid Gigabyte, Palit, Gainward, Galaxy, and MSI has it's own problems. Current gen cards declined quality wise while the reference cards are indeed noisy but are more stable than some of the custom designed cards. I know the gtx 460/560 very well as I am a owner. The main benefit of the reference cards is only the mid plate that cools the vram and power vrm. You have already mentioned one of the downsides of the reference gtx 560 ti and that is the noise generated by the stock fan. Second the cooler is low mass despite the cooper base and heat pipes. Other recommendations are the reference 6870 and 6950 but noise sadly is something you may have to live with due to the cooling needs of modern cards as they consume much more power than previous mid range and low end cards of the last few years. Some were well idiot proof and were great cards but modern cards are the exact opposite even for those who know their stuff. Most have been RMA-ing their cards lately from both so it is no surprise.
Reference gtx 560 ti or go crazy with the mods on a different design. If you want a custom card Asus and MSI are the few choices out there atm that are not to low quality but for them to last they do need some improvement.