diff --git a/lib/shared/thread-utils.js b/lib/shared/thread-utils.js
--- a/lib/shared/thread-utils.js
+++ b/lib/shared/thread-utils.js
@@ -82,7 +82,6 @@
   type ThreadType,
   threadTypes,
   assertThreadType,
-  threadTypeIsThick,
   type ThinThreadType,
 } from '../types/thread-types-enum.js';
 import type {
@@ -169,25 +168,6 @@
   return communityRootMembersToRole;
 }
 
-// This function returns true for all thick threads, as well as all channels
-// inside GENESIS. Channels inside GENESIS were used in place of thick threads
-// before thick threads were launched, and as such we mirror "freezing" behavior
-// between them and thick threads. "Freezing" a thread can occur when a user
-// blocks another user, and those two users are the only members of a given
-// chat. Note that we exclude the GENESIS community root here, as the root
-// itself has never been used in place of thick threads. Also note that
-// grandchild channels of GENESIS get this behavior too, even though we don't
-// currently support channels inside thick threads.
-function threadIsThickOrChannelInsideGenesis(threadInfo: ThreadInfo): boolean {
-  if (threadTypeIsThick(threadInfo.type)) {
-    return true;
-  }
-  if (getCommunity(threadInfo) !== genesis().id) {
-    return false;
-  }
-  return threadInfo.id !== genesis().id;
-}
-
 function useThreadsWithPermission(
   threadInfos: $ReadOnlyArray<ThreadInfo>,
   permission: ThreadPermission,
@@ -197,8 +177,9 @@
 
   return React.useMemo(() => {
     return threadInfos.filter((threadInfo: ThreadInfo) => {
-      const isGroupChat = threadIsThickOrChannelInsideGenesis(threadInfo);
-      if (!isGroupChat || !loggedInUserInfo) {
+      const canBeFrozen =
+        threadSpecs[threadInfo.type].protocol.canBeFrozen(threadInfo);
+      if (!canBeFrozen || !loggedInUserInfo) {
         return hasPermission(threadInfo.currentUser.permissions, permission);
       }
 
diff --git a/lib/shared/threads/protocols/dm-thread-protocol.js b/lib/shared/threads/protocols/dm-thread-protocol.js
--- a/lib/shared/threads/protocols/dm-thread-protocol.js
+++ b/lib/shared/threads/protocols/dm-thread-protocol.js
@@ -729,6 +729,8 @@
 
     couldBeCreatedFromPendingThread: () => true,
 
+    canBeFrozen: () => true,
+
     allowsDeletingSidebarSource: false,
 
     presentationDetails: {
diff --git a/lib/shared/threads/protocols/keyserver-thread-protocol.js b/lib/shared/threads/protocols/keyserver-thread-protocol.js
--- a/lib/shared/threads/protocols/keyserver-thread-protocol.js
+++ b/lib/shared/threads/protocols/keyserver-thread-protocol.js
@@ -40,6 +40,7 @@
 import { getMediaMessageServerDBContentsFromMedia } from '../../../types/messages/media.js';
 import type { RawReactionMessageInfo } from '../../../types/messages/reaction.js';
 import type {
+  ThreadInfo,
   RoleInfo,
   ThreadCurrentUserInfo,
   ThinRawThreadInfo,
@@ -500,6 +501,19 @@
       );
     },
 
+    // Channels inside GENESIS were used in place of thick threads before thick
+    // threads were launched, and as such we mirror "freezing" behavior between
+    // them and thick threads. Note that we exclude the GENESIS community root
+    // here, as the root itself has never been used in place of thick threads.
+    // Also note that grandchild channels of GENESIS get this behavior too,
+    // even though we don't currently support channels inside thick threads.
+    canBeFrozen: (thread: ThreadInfo) => {
+      if (getCommunity(thread) !== genesis().id) {
+        return false;
+      }
+      return thread.id !== genesis().id;
+    },
+
     allowsDeletingSidebarSource: true,
 
     presentationDetails: {
diff --git a/lib/shared/threads/thread-spec.js b/lib/shared/threads/thread-spec.js
--- a/lib/shared/threads/thread-spec.js
+++ b/lib/shared/threads/thread-spec.js
@@ -311,6 +311,9 @@
     input: ProtocolCreatePendingThreadInput,
   ) => RawThreadInfo,
   +couldBeCreatedFromPendingThread: (thread: RawThreadInfo) => boolean,
+  // "Freezing" a thread can occur when a user blocks another user, and those
+  // two users are the only members of a given chat.
+  +canBeFrozen: (thread: ThreadInfo) => boolean,
   +allowsDeletingSidebarSource: boolean,
   +presentationDetails: {
     +membershipChangesShownInThreadPreview: boolean,