It seems to me it's a bug in the documentation.
Currently, column names are not allowed in the LHS (Left Hand Side) of
the formula ('org-table-get-stored-formulas' assumes it). Although I'm
not sure why.
However, the following, with the column name on the RHS, works
|---+----+----+----|
| | 3 | 4 | |
| ^ | c1 | c2 | c3 |
|---+----+----+----|
#+TBLFM: $c3 = $c1 + $c2
Could allowing column names on the LHS in my first example be put on a todo list?
By the way, there is a small error in your example as your $3 should be $4.
Thanks,
Paul