Jeff,
I wish there was a way to prove or disprove this.
Me too.
1) I was going to suggest looking at the Email Delivery History tab for the pending member, to see if Groups.io delivered it to his/her email service successfully or not. But in a trial in my test group just now the pending message isn't logged there one way or another. I'm not sure if that's a bug or a missing feature, but in either case I'm cc'ing this message to support because all such notices ought to be tracked.
2) Said pending message was not received by my test email address. Not Inbox, not Spam. As far as I can determine Groups.io never sent it. Yet I did verify that my test group does have a Pending Subscription notice marked as Active.
So something is rotten, and likely not in Denmark.
One possibility is that I've jumped the gun a bit and the Pending notice has been "greylisted" by my email service: meaning I'll get it later. I'll be disappointed to learn that my email service engages in this practice, but even if it does that initial rejection ought to appear in the Email Delivery History.
Mark:
You should be able to see the activity I've described in shalstest@, if you need more info off-list let me know. Hopefully your logs will show what happened with the pending notice I should have received.
Shal