I know you can call "getChildByName(name)" to access a component (any subclass
of DisplayObject) through it's name property. However,
RadioButtonGroups are not a subclass of DisplayObject, so how can I
programatically get access to them (specifically, so I can clear all buttons
(so none are yet chosen, like at startup).

You can simply set the groups selection parameter to null.
I took the code for the example from Adobe's Flex Documentation and simply
modified it with a button to clear the group.

<?xml version="1.0"?>
<!-- controls\button\RBGroupEvent.mxml -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml">

<mx:Script>
<![CDATA[

import mx.controls.Alert;
import mx.events.ItemClickEvent;

private function handleCard(event:ItemClickEvent):void {
if (event.currentTarget.selectedValue == "AmEx") {
Alert.show("You selected American Express.");
} else if (event.currentTarget.selectedValue == "MC") {
Alert.show("You selected MasterCard.");
} else {
Alert.show("You selected Visa.");
}
}

private function clearRadioGroup(event:Event):void{
this.cardtype.selection = null;
}
]]>
</mx:Script>

<mx:RadioButtonGroup id="cardtype" itemClick="handleCard(event);"/>
<mx:RadioButton groupName="cardtype"
id="americanExpress"
value="AmEx"
label="American Express"
width="150"/>
<mx:RadioButton groupName="cardtype"
id="masterCard"
value="MC"
label="MasterCard"
width="150"/>
<mx:RadioButton groupName="cardtype"
id="visa"
value="Visa"
label="Visa"
width="150"/>
<mx:Button id="clearGroup" label="Clear Group"
click="clearRadioGroup(event)"/>
</mx:Application>

You don't understand what I'm saying... I know how to reset the selection by
setting it to null... What I'm asking is how to get access to the
RadioButtonGroup component programatically... I have a string with the
RadioButtonGroup id... Now give me that component... Like this:

private function(name:String):void
{
// a:RadioButtonGroup = give me the RBG whose id is "name"
a.selection = null
}

If I needed access to a component, I can use getChildByName:

private function(name:String):void
{
a:Label = getChildByName(name) as Label;
a.text = "New label text";
}

But you can't use getChildByName for a RadioButtonGroup... So what do I use
instead, or how can I get the application to return the RBG to me so I can use
it...?

Ah I see what you mean. At least I think I do.
Try this instead.
This is basically the same code as before but notice how I use
this[MY_RADIO_GROUP] in the trace statement to obtain a reference to the
object.

The only thing I do not like about this is you cannot bind the ID param of the
radiobuttongroup to the value of the constant (or variable if you wish).
Perhaps there is a way to do that in MXML but if I need to set that value to a
variable I tend to do it in ActionScript and not in MXML. You CAN however set
the value of the RadioButton.groupName parameters with a Binding if you wish
which can come in handy when dynamically generating a radiobutton that can
change to a different group based on need.

So heres the code. Hope this is what you wanted.

<?xml version="1.0"?>
<!-- controls\button\RBGroupEvent.mxml -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml">

<mx:Script>
<![CDATA[
import mx.utils.ObjectUtil;

import mx.controls.Alert;
import mx.events.ItemClickEvent;

static const MY_RADIO_GROUP:String = "myRadioGroup";

private function handleCard(event:ItemClickEvent):void {
trace(mx.utils.ObjectUtil.toString(this[MY_RADIO_GROUP]));
if (event.currentTarget.selectedValue == "AmEx") {
Alert.show("You selected American Express.");
} else if (event.currentTarget.selectedValue == "MC") {
Alert.show("You selected MasterCard.");
} else {
Alert.show("You selected Visa.");
}
}

private function clearRadioGroup(event:Event):void{
this[MY_RADIO_GROUP].selection = null;
}
]]>
</mx:Script>

<mx:RadioButtonGroup id="myRadioGroup" itemClick="handleCard(event);"/>
<mx:RadioButton groupName="{MY_RADIO_GROUP}"
id="americanExpress"
value="AmEx"
label="American Express"
width="150"/>
<mx:RadioButton groupName="{MY_RADIO_GROUP}"
id="masterCard"
value="MC"
label="MasterCard"
width="150"/>
<mx:RadioButton groupName="{MY_RADIO_GROUP}"
id="visa"
value="Visa"
label="Visa"
width="150"/>
<mx:Button id="clearGroup" label="Clear Group"
click="clearRadioGroup(event)"/>
</mx:Application>