Character Controller Falls Through Colliders

Unity Engine
1

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

using System;
using Rewired;
using UnityEngine;

public class Character : MonoBehaviour
{
    public int playerID = 0;
    public float moveSpeed = 5.0f;
    public float jumpSpeed = 8.0f;
    public float gravity = 20.0f;

    private Player _player;
    private CharacterController _cc;
    private Vector3 _moveVector = Vector3.zero;
    private bool _jump;

    private void Awake()
    {
        _player = ReInput.players.GetPlayer(playerID);
        _cc = GetComponent<CharacterController>();
    }

    private void Update()
    {
        GetInput();
        ProcessInput();
    }

    private void GetInput()
    {
        _moveVector.x = _player.GetAxis(0);
        _jump = _player.GetButtonDown(1);
    }
   
    private void ProcessInput()
    {
        if (_cc.isGrounded)
        {
            _moveVector = new Vector3(_moveVector.x, 0.0f, 0.0f);
            _moveVector *= moveSpeed * Time.fixedDeltaTime;

            if (_jump)
            {
                _moveVector.y = jumpSpeed;
            }
        }

        _moveVector.y -= gravity * Time.fixedDeltaTime;

        _cc.Move(_moveVector * Time.fixedDeltaTime);
    }
}
2

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.