I don't have a finger guard on the lower arm on my machine (it's an "original" Excalibur machine). I suspect that like the NVR switch (which I also don't have), that lower guard is only on the Axi versions (perhaps to meet UK H&S, etc, regs).
With the blade not tensioned, it is, IMO, entirely normal that there should be some side-to-side movement. IMO, what's important is that there is NIL (or virtually NIL) movement when the blade is tensioned. Again that's only IMO, but seems to me perfectly logical (my Manual doesn't say a word about that). Does the Manual for the Axi machine say anything about that?
Re lubrication, in my Manual (pages 17 to 19 inc.) it says that the blade tension lever should be lubricated every 10 to 15 running hours. The "recommended" grease is "white grease" ("petroleum jelly") - or in English, the product is called Vaseline and is available in just about any chemist shop or supermarket. BTW, they also recommend having a spare Blade Tensioning Lever as a stand by spare.
The lubrication of the Upper and Lower Arm pivot bolts, spacers, bearings, and washers is described in my Manual only as "occasional" (which I read as being only "just now and then" - if that's any help)! Again the recommended lubricant for that is "a small blob of white grease", and although my Manual doesn't say so, I've used Vaseline. I think that I've only done that on 2 or perhaps 3 occasions that since the machine was new, nearly 5 years ago now.
I would GUES (just a guess mind) that using any sort of oil is perhaps not such a good idea it is liquid and will act as a "sticky magnet" for saw dust. I would also GUESS that perhaps you're lubricating too frequently, AND that by using oil on the "outside" of the arms only, without disassembling the complete pivots system, that you MAY be adding to the problem ("sticky dust magnet" again). But once more, that's just my guess.
When making that original film I guess that the microphone on the camera was pretty close to those lower arms, Yes? So with the "great big table" directly above the microphone, I guess that would be very likely to amplify whatever noise is already there even more.
I short, IF you have very little to NO side-to-side movement of the arms when the blade is tensioned, then I GUESS you don't really have a problem - and that guess is backed up by listening to your film, when the noise I hear has little or no difference in volume or tone to my own machine.
As said, IF you consider the side-to-side motion too large with the blade in tension, you could try tightening the pivot bolt lock nuts, as per my previous post above.
Lastly, if you're still not happy I would suggest a phone call to Axminster. IME they are very helpful.
HTH - and don't worry, IMO you have a very well engineered machine there.