AFAIK your initial suspicions are correct.
Open Document (for WEBI) doesn’t contain any mechanisms for filtering existing data in the report - it supplies values to prompts, which then affect the query being run, and hence the data returned.
If your query on the linked report takes too long to refresh, investigate the reasons why and address these. If there is too much detail, consider replacing it with a slightly more summarised version and link it to further child reports with increasing levels of detail. Follow best practice to optimise your report, etc.
HTH
NMG
mcnelson 
(BOB member since 2008-10-09)