i don’t think you’re doing anything wrong. although the Identify screen was designed with the “without annotation” parameter, it doesn’t look like the Observation screen was designed to utilize it. it looks like there may have been attempt to implement “without annotation value” parameter (which would be used in conjunction with an annotation parameter, not the without annotation parameter in the Identify screen), but the without value parameter doesn’t appear to work, and i think this has probably been the case for a while:
interestingly, the API’s get observation endpoint seems to be designed to work how the Observation screen was intended to work (as opposed to how the Identify screen works), but it seems to actually work as intended (though that would not bring back the results desired in this situation): http://api.inaturalist.org/v1/observations?place_id=7320&user_id=jbecky&term_id=12&without_term_value_id=13&order=desc&order_by=created_at
you best bet may be to use the Identify screen for now, and maybe request that the Observation screen be updated to work the same as the Identify screen.