Inter-database Stored Procedures And Permissions

Hello all, this is my second post to this newsgroup. It's a question
about stored procedures and permissions and how these behave between
databases.

Here's the scenario. I have a database that stores information for a
system "A", and I have a different database on the same SQL server
that stores the login and other info "LOGIN". I write a stored
procedure in the "A" database that checks some tables in the "LOGIN"
database, let's call this "SP_A".

Additionally I have a user account that accesses all appropriate
stored procedures in "A" called "USER_A", and the same for the "LOGIN"
database, "USER_LOGIN".

Here's the part that raised my curiosity. I log into the server via
Query Analyzer using the "USER_A" account. I run "SP_A" which does a
join between some table in "A" and another table in "LOGIN". I give
"USER_A" execute permission on "SP_A", then I try to run "SP_A" and
get an error:

SELECT permission denied on object '(table in "LOGIN" database)',
database '(real name of "LOGIN")', owner 'dbo'

Huh? how come I need to assign additional select permissions in this
database if I'm not doing an actual select statement? I'm not even
dynamically running a select statement through an exec function. This
just struck me as odd, seeing as how I never explicitly set SELECT
permission on any table in "A" for "USER_A", yet my stored procedure
works, but between databases I have to assign extra permissions for a
stored procedure "SP_A" access to the tables in "LOGIN".

Anyone able to explain this behavior? Because I'm at a loss and I've
only been doing this DB thing for about 2 years.

Thanks in advance, all.
-TJ