I assumed you have unique Clinician_ID, if you don't you need to make sure you do, possibly with the command you suggest.
Actually I was incorrect in the previous message and indeed you are correct. It easy easy to see that if you consider the case where var on the second level is zero(the number of independent units will be number of hospitals and not number of clinicians). The Hospital variable should be ignored only if its ICC is small otherwise the SE will be incorrect. In fact the best practical thing to do is probably ignore the level (level 2 or 3) with smaller ICC. I can't think of an Mplus method that will give you what you want except "TYPE=TWOLEVEL COMPLEX".