All the independents I know all reliably vote Democrat.
In New Hampshire, there is a political party know as Independent; They are very small in number. The voters the author is referring to are actually "undeclared". Being undeclared gives you the option of which party's primary one can vote in; this is useful in local elections.
In any case, undeclared voters do not reliably vote Democrat in New Hampshire.
All the liberals that find New Hampshire quaint, and decide to more here from NY and NJ do reliably vote for Democrats.
See:
New Hampshire Blues: Massachusetts refugees aren't behind the state's liberal drift.