Your grandfather, N.J. Rabensburg, was born in August of 1889; so in 1909 when he left La Grange for Dallas he was as old as 20 (depending on the month). That saddlery in La Grange is the saddlery that he returned to buy from his new uncle-in-law, Louis Walter, after marrying in 1915.
There don't appear, at least from the sources that I can locate including Findagrave, to be more than two men named Arno William Brill. In that case, the first is 'Sr.' and the his son is named is 'Jr.'. To have an Arno William Brill III, there would need to be a third man and he would have to be the son of Jr.
Nevertheless we know from newspaper clippings and the gravestones, that August Brill was known locally (Austin) as Sr., Arno as Jr., and his son Arno was known as 3rd. I will speculate that was simply to help the locals differentiate amongst the three A.W. Brills not least because it was the name on the building :-).
August had three sons and by all three he had grandchildren. The only grandchildren of August (children of Arno) Brill who lived until recently, were Idanell Connally nee Brill (2006) and her brother Bob (2016). We have to take Idanell off the list because her children weren't born Brills. That leaves Bill, and Bob. On closer examination I see that Bill Brill had a son he named Arno William Brill II. Could that "II" (who is not, genealogically) born 1948 have borne a "III"? Could have, but -- he would not actually be a III, and if he was the chap you met, then he was very young. Was he?
So, perhaps, there are now
two tall tales that this man you met, told you: that he was Arno Brill III (who doesn't appear to have ever existed); and that your grandfather didn't succeed the A.W. Brill company (which we all know he did). This is just one piece of the evidence, from 1937:
27 jun 1937 austin american.jpg if it's too small to view, simply close its browser window and it will reappear, larger