@johnna, my apologies for not seeing your question sooner.
I am not familiar with any Google Groups security issues of concern. There were stories last year about companies using GG inadvertently marking their internal groups as public instead of private and so disclosed sensitive information. This, however, was a configuration error and not due to a security issue in GG.
As for signing up to receive our Daily Email, someone does need to “join” to our group. However this is just another name for “subscribing” and is no different from what is required by other platforms used to broadcast emails.