Grant Execute On Sproc Doesn't Grant Privilege To Update?

I am writing a stored procedure which updates a table, but when I run the stored procedure using a login that I have granted execute privileges on, then I get a message that I cannot run an update on the table. This would happen in dynamic sql... while my SQL has parameter references, I don't think it is considered dynamic SQL?

sproc:
CREATE PROCEDURE [schemaname].[SetUserCulture]
@UserID int
, @Culture nvarchar(10)
AS
UPDATE dbo.SecUser
SET Culture = @Culture
WHERE UserID = @UserID

execute SQL:
EXEC schemaname.SetUserCulture @UserID = 9, @Culture = N'x'

error:
The UPDATE permission was denied on the object 'SecUser', database 'DatabaseName', schema 'schemaname'.