2001 Mazda Miata Rattling noise on cold startup

When the Miata is cold or semi-cold there is a very loud rattling noise coming from the engine area. We call it "the diesel" because the noise resembles a semi-trailer diesel engine noise. Otherwise the Miata runs fine performance-wise.

One dealer said it was something like a backpressure oil valve that they see in their CX-7s, the timing cover would have to be removed/might as well replace the timing belt while at it. And $1500 later it is fixed. I believe they are trying to generate revenue for unnecessary repairs.

Could something be loose in the engine or catalytic converter/exhaust system?