Temperatures around 26-28F can mess up the blooms. So can a fungal disease called camellia petal blight (it looks like that may be what the blooms have) and a pest called camellia bud mite.

Camellia Petal Blight info:

https://www.americancamellias.com/care-culture-resources/insects-and-diseases/camellia-petal-blight

Camellia Bud Mites Info:

http://homeguides.sfgate.com/camellia-buds-falling-off-34506.htmlLuis

It can't be the temperature, it never gets so low where I live. The camellia with the problem is right next (leaves touching) to other camellias that don't have any problem; however, they're a different variety. Does this fact eliminate the possibility of blight or mites?

No, not necessarily. The first one to "get" it or "catch" it may simply be Nuccio's Gem. The others could follow this year or next. Depends on how well the fungus reproduces or how well the pests spread. So NG, being close to other camellias, just means that they too will eventually catch it.

FYI: The petal blight disease was once supposedly controlled by preventing contact of infected camellias from one affected area to other areas but the fungus spread anyways and now it is all over.