To be a strategic thinker, and add value to these discussions, it's not so much the message you give, but how you deliver it. When you're exploring an idea, suggestion or concept, there's two key things to keep in mind:
1. Explore through questions - the idea, what's behind it, and it's strategic alignment
2. Explore with curiosity - be genuinely interested in how it all fits.
A useful exploratory question might be "If we do this, will it help us achieve our vision?"
Now try re-reading that question with an emphasis on the words this and vision. See how it starts to sound a bit cynical, disbelieving? Now re-read it putting emphasis on the words we, us and our. How might that sound to someone in a different division or business area? One more - re-read it with emphasis on do and help. Now it sounds like you doubt the idea's relevance, and you think it a poor idea.
So asking the question with genuine curiosity, and a neutral tone, is much more likely to gain a two-way conversation and have you seen as open to ideas. Only once others perceive you have understood and considered their idea, are they open to seeing it may not have strategic alignment. Of course in the process of the conversation you may find that the idea has more merit than you first thought.
Keep exploring the strategic alignment of the idea with curiosity and you'll reach a better decision while developing a reputation as a strategic thinker.