There are a few situation which you might be interested in when it comes to businesses reading your 'text messages'.
They might be able to see your iPhone Messenger messages, if they use the same apple account.
Solution: Setup your own Apple Account and use it for your iMessenger.
If you have your text message synchronizing with your exchange server, your co-workers could read your emails/text messages - If they have access to your exchange account.
Solution: Disable this feature and your will be fine. Your text will stop showing up in your email.
Third Party apps:
If you have a third party app which 'secures' your phone. They may have the option to read your text messages and know your physical location via gps.
Solution: Wipe your phone and start new - do not install apps which are not work related, and do not jail break your phone.
Telus used to give online access to the full 90 day sent and received SMS history on the self service page online. They have since removed users access to those archives as it was a concern for customers and many Telus employees with access to the portal could also bring up customers sms history. Now I believe only the security department at Telus still has access to that tool. You would have to file some kind of legal request for access. But I'm reasonably sure the 90 day sms history is still maintained at Telus, just not as accessible as it once was.
SMS is not a very secure method of communication in general. All service providers and interconnection services involved in transmitting the message can intercept and store them. There is no end to end encryption unless you send your messages pre-encrypted by some means.
Just wait, the tabloids will likely start putting together their own IMSI catchers to spy on celebs sms messages. It will be the next big news ethics scandal. The more sinister spys of the world have already been doing this for years.
i'll throw in my 2 cents on this. Based on your question, it seems that your concern is related to the fact you have a shared plan, and whether this means your text messages are 'shared' or can be viewed across all 3 devices.
First, let's just differentiate between sms text messages and iMessage: sms does not use data so does not fall into your data shared plan. SMS is linked to your phone #, so you only send/recv sms from one device; the other users cannot see your sms text messages from their phones.
iMessage however does use data. The only way your iMessages would show up across all 3 devices is if you linked your personal Apple ID to all 3 devices. In that case, yes, your iMessages would be viewable on all 3 devices.
To avoid this, just make sure each device only has the respective owner's Apple ID associated to it. You can see which devices are associated to your Apple ID by following this guide: https://support.apple.com/en-us/HT204074