diff --git a/Library/Homebrew/diagnostic.rb b/Library/Homebrew/diagnostic.rb
index 902fd8eb33..d2cd19aed5 100644
--- a/Library/Homebrew/diagnostic.rb
+++ b/Library/Homebrew/diagnostic.rb
@@ -884,9 +884,17 @@ module Homebrew
         kegs = Keg.all
 
         deleted_formulae = kegs.map do |keg|
-          next if !CoreTap.instance.installed? && EnvConfig.install_from_api? && Tab.for_keg(keg).tap.core_tap?
+          next if Formulary.tap_paths(keg.name).any?
 
-          keg.name if Formulary.tap_paths(keg.name).blank?
+          if !CoreTap.instance.installed? && EnvConfig.install_from_api?
+            # Formulae installed with HOMEBREW_INSTALL_FROM_API should not count as deleted formulae
+            # but may not have a tap listed in their tab
+            tap = Tab.for_keg(keg).tap
+            next if tap.present? && tap.core_tap?
+            next if tap.blank? && Homebrew::API::Bottle.available?(keg.name)
+          end
+
+          keg.name
         end.compact.uniq
 
         return if deleted_formulae.blank?