With Sony Music swithering between 27 October and 1 November 1983, dmg, I fear that we never know for sure.
There may perhaps be different dates on different documents in their archive. In another example, an 8 May 1985 press release about EMPIRE BURLESQUE says it will be released in "late May". The official release date is 8 June 1985. Obviously, things changed for that album in a very few weeks.
There may also be a difference between the "shipping date" (which I assume to be the day that copies of the album leave the warehouse) and the "in-store date". An additional complication in the past (probably not at the time that INFIDELS was released) was that, at Columbia Records Santa Maria manufacturing plant in California, retailers (and rack jobbers) could just turn up and buy their stock over the counter. Irrespective of the official release date, this could affect availability of albums in shops because shipping could be delayed while the over-the-counter orders/sales were fulfilled.