React & React-Router & Redux rendering of components - reactjs

Question

I have a simple app. It has two components:
Items - it just renders items from the store
AddItem - it just add an item to the store
The question is: why when I submit the form of AddItem component this component is mounted again? If I don't invoke addItem function there is no rerender of AddItem. Any thoughts?
Live example on WebpackBin
Here is the app
import React, { Component } from 'react';
import { BrowserRouter, Match, Link, Redirect, browserHistory } from 'react-router';
import { Provider, connect } from 'react-redux';
import { createStore, bindActionCreators } from 'redux';
import { render } from 'react-dom';
// ACTIONS
const add = (item) => {
return {
type: 'ADD',
payload: item
}
};
// REDUCER
const initialState = {
items: [
'hello',
'world'
]
};
const reducer = (state = initialState, action) => {
switch (action.type) {
case 'ADD': {
return { items: [...state.items, action.payload] };
}
default : {
return state;
}
}
}
// STORE
const store = createStore(reducer);
// ADD ITEM
class AddItem extends Component {
constructor(props) {
super(props);
this.state = {
foo: 'bar'
};
}
componentDidMount() {
console.log('mount AddItem');
}
onSubmit(event) {
event.preventDefault();
this.props.addItem(this.itemTitle.value);
this.form.reset();
this.setState({
foo: 'asd'
});
}
render() {
return (
<div>
<form onSubmit={::this.onSubmit} ref={node => this.form = node}>
<div>
<label htmlFor="item-title">Item</label>
</div>
<div>
<input id="item-title" type="text" defaultValue="baz" ref={node => this.itemTitle = node}/>
</div>
<input type="submit" value="Add" />
<div>
{this.state.foo}
</div>
</form>
<button>Click</button>
</div>
);
}
}
// ITEMS
class Items extends Component {
render() {
return (
<ul>
{
this.props.items.map(item => {
return <li key={item}>{item}</li>;
})
}
</ul>
);
}
}
// LAYOUT
class Layout extends Component {
render() {
const MatchWithProps = ({component:Component, ...rest}) => {
<Match {...rest} render={() => (
<Component {...this.props} />
)}/>
};
return (
<BrowserRouter>
<div>
Reload
<br />
<Link activeOnlyWhenExact activeClassName="active" to="/">Items</Link>
<Link activeClassName="active" to="/add">Add Item</Link>
<hr />
<Match exactly pattern="/" render={() => <Items {...this.props} /> } />
<Match exactly pattern="/add" component={() => <AddItem addItem={this.props.itemActions.add} />} />
</div>
</BrowserRouter>
);
}
}
const mapStateToProps = (state) => {
return {
items: state.items
};
}
const itemActions = { add };
const mapDispatchToProps = (dispatch) => {
return {
itemActions: bindActionCreators(itemActions, dispatch)
};
}
const ConnectedLayout = connect(mapStateToProps, mapDispatchToProps)(Layout);
// PROVIDER
const provider = (
<Provider store={store}>
<ConnectedLayout />
</Provider>
);
render(provider, document.querySelector('#react-container'));