I have never heard of something like that but there may be some truth in it.
The only logical explanation (if it is true) could be because of a starting procedure. Almost by default (do not ask me why) engine #1 (the far left or more correctly starboard engine) is the one, which is started the first (by means of some APU, usually a ground equipment). When running (at some lower rating), again usually, it is utilized to provide power (electric(al) or pneumatic(al)) to start the rest of the engines (one by one). Therefore it could be the most "exploited" engine of all four (if there is no provision in the starting system to alternate the engine which is started the first).
When alternating is mentioned, maybe that would complicate the starting system so much (add weight, reduce reliability etc) that such idea was abandoned a long time ago. Probably something like that draw our sisters and brothers in arms to a decision to sacrifice that #1 and nobody dares to change it.
I am just joking a little bit, but let say for the sake of discussion that it means #1 is operating 1/2 hour longer for every 10 hours of normal operation of the other three engines. That is 5% "overtime" which is probably the same increase in L(ow) C(yclic) F(atigue). Therefore the conclusion is: engines should be rotated like tires every 250 000 miles or 1000 hrs whichever comes the first.
The other reason could be Coriolis' load (force) which is larger for outer engines during roll and yaw (so it applies to both #1 and #4). That Coriolis' acceleration I have never understood and you will have to enlighten me if you could.
A "critical" engine typically refers to the engine with the propeller down-stroke closest to a multi-engine plane's centerline. In a twin-engine plane, single-engine operations are determined based on loss of the critical engine, i.e. worst case scenario.
