There are no dumb questions. If the question occurred to you then obviously something was not made clear in the first place. Of course this does not apply to questions made in bad faith as it were.
It gets boringly technical, but you are correct that the supplied resistor in the common of the eBay signal head demotes the effect of the AC. BUT, to your point, a demotion from sergeant to corporal is not the same as being dishonorably discharged! I think what can be 100% agreed upon is that inserting a 5-cent diode is cheap insurance. That you have to buy some minimum quantity or pay disproportionate shipping charges is another matter!
As to the voltage rating of the 1N4007 vs. a different 1N400x. Yes, there's more techno-speak that the cognoscenti can elaborate on. As it turns out, we're talking about 14V AC or maybe 18V AC at most. 100V, 200V, 1000V are all more than adequate for the task. Frankly, I've never heard of choosing a part using a 10X rule...but that's just me. 2x or 3x in this case is fine in my opinion.
So the next question is whether there's any downside in using using a 1000V part for a 14V application. Well, in this particular application NO. There are applications where you might pay a technical penalty (e.g., wasted power)...but your application is NOT one of them. It practically comes down to what you can get a good "deal" on!
It does kind of bother me that you are paying $3.78 for what might effectively amount to 1 diode (if you don't have another application for the extras). That's more than what you'd pay at Radio Shack which is valiantly making its comeback!
I buy 1N400x diodes for less than a penny a piece but then I use them in quantity. If you're really going to spend $3.78 for 1 diode 
, I will send you some diodes absolutely FREE! Just paypal me the 75 cents (or whatever it is) for a non-machinable postage stamp. Hmmm I don't know if paypal allows such a minimal transaction?! 
