Do statistics referencing a column prevent that column from being dropped?

I'm trying a very simple drop column statement:

alter table MyTable drop column MyColumn

and receiving several errors along the lines of

Msg 5074, Level 16, State 1, Line 1
The statistics '_dta_stat_1268251623_3_2' is dependent on column 'MyColumn'.

followed ultimately by

Msg 4922, Level 16, State 9, Line 1
ALTER TABLE DROP COLUMN MyColumn failed because one or more objects access this column.

I didn't think statistics prevent a column from being dropped. Do they? If so, since these are apparently auto-created statistics I can't depend on the names being the same across multiple copies of the same database, so how could I drop all such statistics in an upgrade script to be executed on a different database?