Since taking up BP shooting in 1973, I've had the understanding the reason for no petrolium products is that petrolium products will not mix with bp fouling to soften it. I have never heard of this turning to asphault or any other problem, just that petrolium does not mix - therefore do not use it as it doesn't work- ie: for lube.
I have used BreakFree BLC and other products for an after clean and dry preservative in the past, but now it's WD40 and that's it - it works for me- and Taylor and LB and everyone else in the club here.
The only pretrolium product that works with BP fouling that I know of, is Vaseline when mixed with melted BeesWax as a bullet lube - 60:40 - it works - don't know why - but the stuff I mixed up is just as good as the other BP lubes I tried, SPG or Lyman's BPGold - in both of my rifles - a .45/60 Sharps and a .50 Alaskan chambered Rolling Block. Your milage might vary.
I have adhered to the no-petrolium products as noted above, and this has worked perfectly for me - no asphault - must work.
Motor oil is a very poor rust preventer as far as I know as engine blocks will rust underneath a coating of the stuff. Now, that might be due to used oil having corrosives, by-products of combustion in them - perhaps fresh oil is OK- doubt it.
Most of the better motor oils today are partical synthetics & total synthetics (even if they don't say so) - good motor oils have synthetic additives to withstand the engine temps produced today, especially in bearing races, in the heads. Petrolium oils turn to asphault at something like 300F to 310F - normal temps in the bearing races can easily ecceed those temps - therefore synthetics or synthetic additives are required. I like Amsoil myself. Been using their products it since 1977 and love 'em - change oil once a year and never burn oil - even at over 200,000 miles. I don't use them for patch lube or an after-oil - don't need them, WD40 works for me.