Shouldn't RAM (Random Access Memory) be called AAM (Arbitrary Access Memory)?

Quoting the accepted answer from this, the explanation to why 'RAM is random' is this:

whatever location in the RAM you want to access, you get to it in constant time (as opposed, for example, to a tape drive, where the seek time depends from the actual length of tape you have to move to get there).

Now, for "regular" RAM this property is (at least AFAIK) true - when the processor/motherboard/memory controller asks to a RAM chip to get some data, it does so in constant time;

However, considering the difference between random and arbitrary, as it is widely perceived and imo best put by a Y!Answer:

Random means without any specific choice whereas arbitrary means based on one's whims and fancies.

, then I think this name - Random Access Memory is erroneous.

If you consider the fact that the exact address of what you want to retrieve from the memory is indeed unknown to you, then you might indeed legitimately call it random. However, it is called this way from the sole purpose of differentiating it from other memory types, in which you "can't instantly access a specific, arbitrary portion/part from it (i.e. on tapes you need to rewind until you find your song)". Taking this into account, in RAM - you can. So, "you can instantly arbitrarily access any portion of the memory".

And moreover, wouldn't random access imply random values also?