When no on-call user is available, incoming call routing redirects the caller to leave a voicemail. Then, a link to the voicemail on Twilio is added to the related alert.

The message below is included in the voicemail settings and is confusing as the voicemails are not actually attached:

Redirects the caller to leave a voicemail if no user is available. The recorded voicemail is attached to the alert. If disabled, ends the call instead.

Suggestion  

Create the ability to include the actual voicemail file as an attachment in the alert instead of the URL so users don't need to authenticate on Twilio to hear the message.