Do you think straps make your Rolex more "under the radar"?

[the dark knight]

I see questions (more often these days it seems) asking which model of Rolex is more or most "under the radar", people desiring this for various reasons.

Often the responses are Explorer I, OP, etc.

But I'm now of the opinion you should just buy the exact model you want and just put it on a strap if you want to be under the radar. I dare say an Exp I on the Oyster is more recognizable as a Rolex than, say, a BLRO put on a leather strap.

I think this works even on PM models, I think Day-Dates look really sharp on the right leather.

Thoughts on this?