I had a similar issue. The query provided earlier is not quite right. Here is the correct query:
SELECT SCHEMA_NAME(tab.schema_id) SchemaName
, tab.name TableName
, col.column_id ColumnId
, col.name ColumnName
, s.name StatsName
, s.auto_created AutoCreated
, 'DROP STATISTICS ' + SCHEMA_NAME(tab.schema_id) + '.' + tab.name + '.' + s.name DropStatSQL
FROM sys.tables tab
JOIN sys.columns col ON tab.object_id = col.object_id
JOIN sys.stats_columns sc ON col.column_id = sc.column_id
AND col.object_id = sc.object_id
JOIN sys.stats s ON sc.stats_id = s.stats_id
AND s.object_id = sc.object_id
WHERE tab.name = 'YourTableName'
AND col.name = 'YourColName'
The StatsName in this query did not match the name of the stats in the error message but I tried dropping the AutoCreated statistic for the column anyway and I was then able to drop the column in the table.
Perhaps the stat name we get in the error message (in format stat_..... ) is just an alias for the real stat name.