This is definitely not true. There are context-free grammar and finite state machines are not Turing complete (TC). Strong functional programming languages (always terminate and every action is defined: e.g. x/0=0) are not TC since they exclude the ability to not terminate. In fact, most things you run on a computer are not TC as they are deterministically terminating. Computers themselves are not TC! They have finite memory. For practical purposes they are, and the languages they use often are, but I'd be a bit careful with your "personal theory" as it doesn't capture the ideas of TC that well.