запускай с указанием владельца типа exec dbo.sp1

Из BOL:

Database Owner (dbo)

The dbo is a user that has implied permissions to perform all activities in the database. Any member of the sysadmin fixed server role who uses a database is mapped to the special user inside each database called dbo. Also, any object created by any member of the sysadmin fixed server role belongs to dbo automatically.

For example, if user Andrew is a member of the sysadmin fixed server role and creates a table T1, T1 belongs to dbo and is qualified as dbo.T1, not as Andrew.T1. Conversely, if Andrew is not a member of the sysadmin fixed server role but is a member only of the db_owner fixed database role and creates a table T1, T1 belongs to Andrew and is qualified as Andrew.T1. The table belongs to Andrew because he did not qualify the table as dbo.T1.

The dbo user cannot be deleted and is always present in every database.

Only objects created by members of the sysadmin fixed server role (or by the dbo user) belong to dbo. Objects created by any other user who is not also a member of the sysadmin fixed server role (including members of the db_owner fixed database role):

Belong to the user creating the object, not dbo.

Are qualified with the name of the user who created the object.

Всмысле не обязательно dbo. Владелец может быть и другой. Главное явно указать владельца, чтобы сервер эту процедуру нашел.