Beltrami57, texts are viewable online via My Verizon only for the number that is logged in. If you wish to secure information, you would want to ensure you have a login password known only by you. (see link below) To clarify, the Account Owner can view dates/times of messages sent via the Account Management section.
https://www.verizon.com/support/knowledge-base-217522/
*Joshua
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