If you can identify your customer, the account, and the transaction(s) in question, the customer has provided everything (s)he is required to provide. If you require anything further before you accept a claim, you are in violation of Reg E - including requiring a specific form.
You're correct that it's common practice to ask for a specific form with tailored questions. We do it here, too. The key word is ask - not require. Most of the time your customers are more than willing to provide the information, just remember in the case of a phone call notification you are effectively notified and should begin your investigation. If you have disclosed and require written notification, then you can withhold provisional credit - but otherwise you're on the hook. If you're notified by email, that's generally going to be considered written notification (at least that's our interpretation here).
If it helps, we use our dispute forms for every single dispute. If we get a call, our reps fill in the form, record the date of the call, and forward to our dispute dept. If an email, we print the email and keep it with the file, but transfer the information to our dispute form. If a customer actually drops off some kind of written notification (happens once in a blue moon, usually a statement with transactions circled with some iteration of "I didn't do this") we transfer the info to our dispute form. See the pattern? We do require the use of our forms for consistency...we just don't require our customers to fill it in.
I reject your reality and replace it with my own.