Simple search in our database is completely unusable as well, and I think our problems are related to the issue as you are describing. 
I often forget about it because it has never worked since we’ve adopted specify, but it is very confusing for lay users, especially because it cannot be removed entirely from the GUI in 7.
To my knowledge, Simple Search was user-configurable in Specify 6, but is not yet user configurable in 7, at least not in the front end. I am unsure whether the issues we experience can be fixed by altering configuration in Sp6, but @Grant or @bhumikagupta should be able to tell you.
When we search pretty much anything it just returns the record most closely matching the search term in the most granular table in which the term occurs (for example, searching “Amblema” doesn’t bring up lots that are identified as Amblema plicata, or lots identified as Amblema sp., it only brings up the genus record for Amblema in the taxon table, and then links 628 completely unrelated taxa in the taxon tree as well.
e.g. https://invertebrates.osu.edu/specify/simple-search/?q=amblema
It seems these 628 taxa get linked no matter what you search. That seems new to me… but I don’t use Simple Search often enough to know if and when the behavior changed.
see also https://invertebrates.osu.edu/specify/simple-search/?q=Ohio+River
Multiple collections requesting a fix will bump this up on the devs’ radar. They have been doing a bang up job this year in rolling out new features, so hopefully this gets fixed soon.