Yes I have heard the same but never read of any actual occurrences. The Haynes 190E (W124) manual has a good write up on changing a single row chain on a 102 motor, and that part of the engine is identical to yours. At 250km it might be time.
The only extra I would add to the published procedure is that prior to starting, be thoroughly conversant with the valve and ignition timing of your engine (if you are not already). Because if you stuff it up and drop one end of the chain into the guts of the motor, its a lot less stress to get back to where it needs to be if you are prepared. Valve timing is easy: set the crankshaft at TDC and check the line on the camshaft lines up. Ignition timing at TDC; take the distributor cap off and observe the rotor pointing to the line on the distributor plate, use a rule to accurately measure the gap either side of the adjustment lock down bolt. Take photo's if necessary.
These are an interference motor, without a chain you will have problems winding over the crank independent of the cam and vice versa.
Also, before you grind off a rivet, wind the chain through its length just to make sure it does not have a quick link fitted; originals won't have but a few after market chains do.
When I first did this job I got advice from an MB agency supervisor (it was a small town in a small country) and he said they always fit a new timing chain tensioner when fitting a new chain because it avoided potential problems with warranty claims. I now have a bag of chain tensioners that look fine to me, but it may be worth thinking about.