The offending company didn't begin with a 'C' did it?
I also have problems with mail order plants, I purchased a Jasminum officinale from a company, and it died recently, not acceptable really so I know how frustrating it is.
Have you asked the company for a refund, if you have the invoice still I would have thought you are entitled to it, either that or you could get a perennial plant for the same value as the Begonias (although no certainties it will be any higher in quality).
I suppose it's best buying from nurseries/garden centres. I certainly won't be buying online again.