diff --git a/dvc/repo/index.py b/dvc/repo/index.py
index b3dfb47ee..bac2bfa36 100644
--- a/dvc/repo/index.py
+++ b/dvc/repo/index.py
@@ -221,7 +221,7 @@ def _load_storage_from_out(storage_map, key, out):
                     ),
                 )
             )
-        storage_map.add_remote(FileStorage(key, dep.fs, dep.fs_path))
+        storage_map.add_remote(FileStorage(key, dep.fs, dep.fs_path, read_only=True))
 
 
 class Index:
diff --git a/pyproject.toml b/pyproject.toml
index 54c1b4614..95e30fe91 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -35,7 +35,7 @@ dependencies = [
     "configobj>=5.0.6",
     "distro>=1.3",
     "dpath<3,>=2.1.0",
-    "dvc-data>=3.4,<3.5",
+    "dvc-data>=3.5,<3.6",
     "dvc-http>=2.29.0",
     "dvc-render>=1.0.0,<2",
     "dvc-studio-client>=0.17.1,<1",
diff --git a/tests/func/test_repo_index.py b/tests/func/test_repo_index.py
index 9a0b06ea4..42a5123a2 100644
--- a/tests/func/test_repo_index.py
+++ b/tests/func/test_repo_index.py
@@ -1,3 +1,4 @@
+import os
 from itertools import chain
 
 import pytest
@@ -338,3 +339,53 @@ params:
     tmp_dir.gen("dvc.yaml", top_level_params)
     index = Index.from_repo(dvc)
     assert index.param_keys == {"repo": {("classifier", "custom_params_file.yaml")}}
+
+
+def test_data_index(tmp_dir, dvc, local_cloud, erepo_dir):
+    tmp_dir.dvc_gen(
+        {
+            "foo": b"foo",
+            "dir": {"bar": b"bar", "subdir": {"baz": b"baz"}},
+        }
+    )
+
+    with erepo_dir.chdir():
+        erepo_dir.dvc_gen("efoo", b"efoo", commit="create efoo")
+        erepo_dir.dvc_gen(
+            "edir",
+            {"ebar": b"ebar", "esubdir": {"ebaz": b"ebaz"}},
+            commit="create edir",
+        )
+
+    dvc.imp(os.fspath(erepo_dir), "efoo")
+    dvc.imp(os.fspath(erepo_dir), "edir")
+
+    local_cloud.gen("ifoo", b"ifoo")
+    local_cloud.gen("idir", {"ibar": b"ibar", "isubdir": {"ibaz": b"ibaz"}})
+
+    dvc.imp_url(str(local_cloud / "ifoo"))
+    dvc.imp_url(str(local_cloud / "idir"))
+
+    index = Index.from_repo(dvc)
+    assert index.data_keys == {
+        "local": set(),
+        "repo": {("dir",), ("edir",), ("efoo",), ("foo",), ("idir",), ("ifoo",)},
+    }
+
+    data = index.data["repo"]
+    assert set(data.keys()) == {
+        ("dir",),
+        ("edir",),
+        ("efoo",),
+        ("foo",),
+        ("idir",),
+        ("ifoo",),
+    }
+
+    assert not data.storage_map[("foo",)].remote
+    assert not data.storage_map[("dir",)].remote
+
+    assert data.storage_map[("efoo",)].remote.read_only
+    assert data.storage_map[("edir",)].remote.read_only
+    assert data.storage_map[("ifoo",)].remote.read_only
+    assert data.storage_map[("idir",)].remote.read_only