Re: Not receiving text messages from web sites
The only likely possibility I could think of with the phone is parental controls, as tsac mentioned first, but which you have ruled out, I think. That is, it isn't an issue of receiving or not receiving messages from sends in your address book or not.
Regarding short codes, I know the messages I get from T-Mobile show short codes as the sender instead of full phone numbers. Same thing with the two-factor verification codes I get from other services. I assume AT&T does the same thing, and that when they sent the test message to you it would have displayed to you as a short code for the sender. I don't know the differences in the case of short codes over regular SMS/MMS sent from a phone. I've wondered if maybe short codes are like personalized license plate, or custom PIN's. Maybe there is a glitch in that registry at AT&T, except there shouldn't be a problem with their short code in their own registry. So, I really have no idea, but it seems a factor, and that is part of what makes me wonder if that this key to the problem. And yes, I would have expected AT&T to clue in on this, and maybe they have and that is what they are looking at, or one of the things.
I don't recall on the legacy BBOS, maybe it is there, but on BB10 in the SMS/MMS settings there is an option for Routing Preference (Packet Switched/Circuit Switched/Packet Switch Preferred/Circuit Switch Preferred). It wouldn't hurt to play with this, if it is there in BBOS, though I doubt it is the issue. For me SMS/MMS work on the mobile network either way, and the difference is when on wi-fi calling.
Now that I'm thinking more outside the box, something else you can try, if you have the option in BBOS, is change the Network Mode. I don't think this should make a difference in your case, but at this point try what you can and see what happens. (What makes me think of this is I have had problems sending texts in some locations, rarely, and the solution is changing the Network Mode from 4GLTE & 4G/3G & 2G to something else. It's a different problem than you are having, but there is a hint of possibility.)
Last edited by aiharkness; 12-09-2018 at 09:12 AM..