Setting up filtering for server-side tracing
Does that mean the server-side trace is always only checking the database it's been creating in?


No, the server-side trace has the scope of just that:  the server.  When I create (what I think is) the exact trace definition and export it, I get the following snippet:

-- Set the Filters
declare @intfilter int
declare @bigintfilter bigint

set @bigintfilter = 1000000
exec sp_trace_setfilter @TraceID, 13, 0, 4, @bigintfilter

exec sp_trace_setfilter @TraceID, 35, 0, 6, N'AdventureWorks'
-- Set the trace status to start
exec sp_trace_setstatus @TraceID, 1


I am using SQL Server Profiler 2008 R2 as well.  If you do not filter on the database name, then you will be capturing trace events for all of the instance databases.  As to why your export didn't seem to include that portion of the filter, I can't say for sure.  I know this goes without saying, but I'd check your trace definition within Profiler before you export to ensure the database name is in fact included as a filter (again, I know you've probably double and tripple checked this, but I had to say it).