Verizon should allow someone to have the option to send a muted text. This would allow people on night shift to send important messages that will be waiting for the recipient without the possibility of waking them up. Would also be helpful for people at work or in church who may forget to turn their ringer off.
This isn't a Verizon thing. It wolud be something the messaging app would have built into it. And it would also requir the recipient to have a messaging app that allows this.
So what you are asking is for Verizon to somehow allow someone aside from yourself to affect the settings on YOUR phone in order to notify you in some other way than how YOU have chosen to have your phone notify you of an incoming text???? If someone wants their phone to make a sound for an incoming message, who are YOU to say their phone shouldn't do so? I don't think that is going to be very popular among most users.
I prefer that I choose the settings on my phone about how I am notified for incoming messages.
With your suggestion, if someone were able to force your phone to "mute" a message wouldn't it also be plausible to force your phone to make an audible sound when a message arrives if the sender thought the message was important enough to do so? Having someone else determine how your phone reacts to an incoming message is not something many people would be happy to allow, myself included.