Character Controller Falls Through Colliders

I have a model (a Mixamo Fuse character, with animations), which has on it a Character Controller, a script, and which is a child of an empty game object. It does not have on it a Rigidbody of any kind. All my collision layers are set to collide with each other. My character is positioned 1 unit above a plane which has on it a mesh collider. And yet, when I press play, the character falls until half its body is embedded into the plane, then stops. I can move around normally, but remain inside the plane. Below is the script for reference. Unity version is 2019.3.0b12

Code (CSharp):

1. using System;
2. using Rewired;
3. using UnityEngine;
4.  
5. public class Character : MonoBehaviour
6. {
7.     public int playerID = 0;
8.     public float moveSpeed = 5.0f;
9.     public float jumpSpeed = 8.0f;
10.     public float gravity = 20.0f;
11.  
12.     private Player _player;
13.     private CharacterController _cc;
14.     private Vector3 _moveVector = Vector3.zero;
15.     private bool _jump;
16.  
17.     private void Awake()
18.     {
19.         _player = ReInput.players.GetPlayer(playerID);
20.         _cc = GetComponent<CharacterController>();
21.     }
22.  
23.     private void Update()
24.     {
25.         GetInput();
26.         ProcessInput();
27.     }
28.  
29.     private void GetInput()
30.     {
31.         _moveVector.x = _player.GetAxis(0);
32.         _jump = _player.GetButtonDown(1);
33.     }
34.    
35.     private void ProcessInput()
36.     {
37.         if (_cc.isGrounded)
38.         {
39.             _moveVector = new Vector3(_moveVector.x, 0.0f, 0.0f);
40.             _moveVector *= moveSpeed * Time.fixedDeltaTime;
41.  
42.             if (_jump)
43.             {
44.                 _moveVector.y = jumpSpeed;
45.             }
46.         }
47.  
48.         _moveVector.y -= gravity * Time.fixedDeltaTime;
49.  
50.         _cc.Move(_moveVector * Time.fixedDeltaTime);
51.     }
52. }
53.  

 

Update

I added a few animations and an animation controller, wrote a few extra lines of code to control a couple animator parameters, and now the character floats slightly above the ground instead of getting embedded in it. The collider has not changed at all. If I view it while the game is running, it very clearly is not touching the ground.