That's because double quotes is considered standard while single quote is not. This is not really specific to JQuery, but its about JSON standard. So irrespective of JS toolkit, you should expect same behaviour.
A value can be a string in double quotes, or a number, or true or false or null, or an object or an array. These structures can be nested.
Go to www.Jsonlint.com website and check your single quotes json string you will found that it is not a valid json string. Because double quotes json is standard json format.
jsonlint.com is a website to check json format right or not.