diff --git a/src/H5Dint.c b/src/H5Dint.c
index 37c9fe490a8..3b9d000f523 100644
--- a/src/H5Dint.c
+++ b/src/H5Dint.c
@@ -947,8 +947,8 @@ H5D__update_oh_info(H5F_t *file, H5D_t *dset, hid_t dapl_id)
         HGOTO_ERROR(H5E_DATASET, H5E_CANTPIN, FAIL, "unable to pin dataset object header");
 
     /* Check for creating dataset with unusual datatype */
-    if (H5T_is_numeric_with_unusual_unused_bits(type) &&
-        !(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)))
+    if (!(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)) &&
+        H5T_is_numeric_with_unusual_unused_bits(type))
         HGOTO_ERROR(H5E_DATASET, H5E_CANTINIT, FAIL,
                     "creating dataset with unusual datatype, see documentation for "
                     "H5Pset_relax_file_integrity_checks for details.");
diff --git a/src/H5Oattribute.c b/src/H5Oattribute.c
index 64634aac405..4929be56717 100644
--- a/src/H5Oattribute.c
+++ b/src/H5Oattribute.c
@@ -212,8 +212,8 @@ H5O__attr_create(const H5O_loc_t *loc, H5A_t *attr)
         HGOTO_ERROR(H5E_ATTR, H5E_CANTPIN, FAIL, "unable to pin object header");
 
     /* Check for creating attribute with unusual datatype */
-    if (H5T_is_numeric_with_unusual_unused_bits(attr->shared->dt) &&
-        !(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(loc->file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)))
+    if (!(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(loc->file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)) &&
+        H5T_is_numeric_with_unusual_unused_bits(attr->shared->dt))
         HGOTO_ERROR(H5E_ATTR, H5E_CANTINIT, FAIL,
                     "creating attribute with unusual datatype, see documentation for "
                     "H5Pset_relax_file_integrity_checks for details.");
diff --git a/src/H5Tcommit.c b/src/H5Tcommit.c
index 2e23764fa7a..00a88984375 100644
--- a/src/H5Tcommit.c
+++ b/src/H5Tcommit.c
@@ -490,8 +490,8 @@ H5T__commit(H5F_t *file, H5T_t *type, hid_t tcpl_id)
         HGOTO_ERROR(H5E_ATTR, H5E_CANTPIN, FAIL, "unable to pin object header");
 
     /* Check for creating committed datatype with unusual datatype */
-    if (H5T_is_numeric_with_unusual_unused_bits(type) &&
-        !(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)))
+    if (!(H5O_has_chksum(oh) || (H5F_RFIC_FLAGS(file) & H5F_RFIC_UNUSUAL_NUM_UNUSED_NUMERIC_BITS)) &&
+        H5T_is_numeric_with_unusual_unused_bits(type))
         HGOTO_ERROR(H5E_DATATYPE, H5E_CANTINIT, FAIL,
                     "creating committed datatype with unusual datatype, see documentation for "
                     "H5Pset_relax_file_integrity_checks for details.");