Execution Plan not matching Stored Proc
Your code says you are doing a LEFT OUTER JOIN, but are you really? Your very first WHERE clause (as well as each that follow) filters rows for inclusion from the outer table:

WHERE     (A.[Operator_Name] LIKE '%'+ @OName +'%')


This turns your LEFT OUTER JOIN into an INNER JOIN, whether you meant it or not. Perhaps you meant to move those filters to the ON clause.

Of course I would probably remove the non-sargeable MONTH() function from the JOIN, since this is going to force a complete scan on the remote table, and write it this way instead - also eliminating the join to your local months table:

DECLARE 
  @OName      VARCHAR(50) = 'John', 
  @Start_Date DATE = NULL,--'20120101', -- use safe date formats 
  @End_Date   DATE = '20121231'; -- use semi-colons

-- deal with NULLs here so the query is simpler:

SELECT @Start_Date = COALESCE(@Start_Date, '20010101'),
       @End_Date   = COALESCE(@End_Date, CURRENT_TIMESTAMP);

;WITH n(n) AS 
(
  -- get the # of months you need instead of relying on your Connector table:
  SELECT TOP (DATEDIFF(MONTH, @Start_Date, @End_Date)+1) Number
    FROM master..spt_values
    WHERE [type] = N'P' AND Number &gt;= 0
    ORDER BY Number
), m(m) AS
(
  -- convert those to months:
  SELECT DATEADD(MONTH, n, DATEADD(MONTH, DATEDIFF(MONTH, 0, @Start_Date), 0))
  FROM n
)
SELECT 
  m.m, 
  MonthName = DATENAME(MONTH, m.m),
  [Widget Count] = COUNT(w.Widget_ID)
FROM m
LEFT OUTER JOIN [Server].[Database].dbo.Widget AS w -- meaningful alias
ON 
  w.Widget_Date &gt;= m.m
  AND w.Widget_Date &lt; DATEADD(MONTH, 1, m.m) -- open-ended date range query
  AND w.Operator_Name LIKE '%' + @OName + '%'
GROUP BY m.m
ORDER BY m.m;


Just ignore the m column in the output (you can't order by it without including it in the output, and it doesn't make sense to order by the name).

Another suggestion: don't use 'single quotes' as alias delimiters. Forms of this are deprecated and it also makes column alias look like string literals. Use [square brackets] instead.