I'm with OpsGenie. Some background information may be useful. OpsGenie - SolarWinds WHD integration has 2 data flows.
1. WHD creates alerts in OpsGenie. This data flow is initiated by WHD which sends an email to OpsGenie. No network changes, IP etc. is needed since it only needs WHD to be able to send email.
2. When a user adds a note to the alert in OpsGenie, OpsGenie can make a web request to the WHD and update the ticket with the note. For this to work, WHD does indeed need to have a web URL that is accessible from the web. If you're looking for this functionality, feel free to make an enhancement request via support at opsgenie.com. We have a utility that initiates the connection to our servers hence it's possible to implement this functionality in a way that would work with an internal WHD instance without changing any network, firewall, etc.
Thanks for the information. Very helpful for our evaluation of Ops Genie.