It sounds like there are different owners of the procedure as well as the underlying object that the SELECT is querying. This all has to do with Ownership Chains. See the below example for a brief explanation and demonstration to what I'm talking about:
use YourTestDatabase;
go
create login TestLogin1
with
password = 'password',
check_policy = off;
go
create user TestUser1
for login TestLogin1;
go
create table Table1
(
id int identity(1, 1) not null,
SomeString varchar(30) not null
default replicate('a', 30)
);
go
insert into Table1
values(default);
go 10
create proc Proc1
as
select *
from Table1;
go
grant execute
on Proc1
to TestUser1;
go
-- this works because permissions aren't checked
-- on Table1. That is why TestUser1 can get the
-- result set without SELECT permissions on Table1
execute as user = 'TestUser1';
go
exec Proc1;
go
revert;
go
-- let's change the owner of Proc1 so that the
-- ownership chain is broken and permissions are
-- checked on Table1
alter authorization
on Proc1
to TestUser1;
go
-- this no longer works because permissions are now
-- checked on Table1, which TestUser1 does not have
-- SELECT permissions on
execute as user = 'TestUser1';
go
exec Proc1;
go
revert;
go
If you want to find out the ownership of your objects, you can run the below query (obviously with changing the WHERE clause to include your specific object names):
select
o.name,
o.type_desc,
case
when o.principal_id is null
then sp.name
else dp.name
end as principal_name
from sys.objects o
inner join sys.schemas s
on o.schema_id = s.schema_id
left join sys.database_principals dp
on o.principal_id = dp.principal_id
left join sys.database_principals sp
on s.principal_id = sp.principal_id
where o.name in
(
'Table1',
'Proc1'
);