diff --git a/libcudacxx/include/cuda/__mdspan/host_device_accessor.h b/libcudacxx/include/cuda/__mdspan/host_device_accessor.h
index 4edbe9972db..b7fd5cc3dc0 100644
--- a/libcudacxx/include/cuda/__mdspan/host_device_accessor.h
+++ b/libcudacxx/include/cuda/__mdspan/host_device_accessor.h
@@ -196,7 +196,10 @@ class __host_accessor : public _Accessor
   _CCCL_API constexpr reference access(data_handle_type __p, ::cuda::std::size_t __i) const
     noexcept(__is_access_noexcept)
   {
-    NV_IF_TARGET(NV_IS_DEVICE, (_CCCL_VERIFY(false, "cuda::__host_accessor cannot be used in DEVICE code");))
+    _CCCL_IF_NOT_CONSTEVAL_DEFAULT
+    {
+      NV_IF_TARGET(NV_IS_DEVICE, (_CCCL_VERIFY(false, "cuda::__host_accessor cannot be used in DEVICE code");))
+    }
     return _Accessor::access(__p, __i);
   }
 
@@ -217,7 +220,7 @@ class __host_accessor : public _Accessor
       _CCCL_ASSERT(__is_valid, "host_accessor (mdspan): data handle doesn't point to a valid host memory");
       return !__is_valid;
     }
-    return true;
+    return false;
   }
 #endif // !defined(_CCCL_DISABLE_MDSPAN_ACCESSOR_DETECT_INVALIDITY)
 };
@@ -352,7 +355,7 @@ class __device_accessor : public _Accessor
                    "device_accessor (mdspan): data handle doesn't point to a valid device or managed memory");
       return !__is_valid;
     }
-    return true;
+    return false;
   }
 #endif // !defined(_CCCL_DISABLE_MDSPAN_ACCESSOR_DETECT_INVALIDITY)
 };
@@ -472,7 +475,7 @@ class __managed_accessor : public _Accessor
       _CCCL_ASSERT(__is_valid, "managed_accessor (mdspan): data handle doesn't point to a valid managed memory");
       return !__is_valid;
     }
-    return true;
+    return false;
   }
 #endif // !defined(_CCCL_DISABLE_MDSPAN_ACCESSOR_DETECT_INVALIDITY)
 };