I used to believe that myself. As far as I've been able to determine, that date seems to originate from Greg Theakston, who mentioned it in Pure Images #2 circa 1991. My guess is that he got the date by finding the earliest records he could of a newsstand receiving their copies.
But that's not entirely accurate.
See, back in 1961, there wasn't a single distributor system for comics like there is now. Not to mention what was available worked much slower. So different newsstands and drug stores got their shipments on different days. Generally kind of close to one another, just not on the same day. One shop might get their books on a Tuesday, the guy in the next city might get his on Wednesday, and the guy in the city after that might be on Thursday.
There was also poor communication to the retailers. They didn't necessarily know what they would get on any given delivery, or when the next shipment of a particular title might come in. Since all the comics (and magazines) were returnable, this wasn't a big deal. But retailers did need to know when it might be okay to send old books back, so they would often write or stamp the date they received them on the cover. (Collectiblity was obviously not a concern.) Then, as they were surveying their stock, they could easily determine that it had only been three weeks since they got this issue, but maybe ten weeks since they got this other one. But, here and now, decades later, we can use those same markings to determine when certain issues hit the stands!
Which leads us to Fantastic Four #1. If the copies of the version Theakston saw in the late '80s and early '90s had nothing earlier than an August 8th date, it's reasonable to conclude that that was the earliest anyone got it. However, since then -- thanks in large part to the internet -- we've uncovered examples of other copies with other dates, such as August 1st, 3rd, 8th, 9th, and as late as the 21st. I've even found one marked July 3its0th! (I haven't done a comprehensive search; it's possible there are even earlier dates.) Which means, if the title hit some of the newsstands as early as July 30, then claiming the FF's anniversary is August 8th means you're off by at least a full week.
It's a minor point, to be sure, but if you're going to go around celebrating the exact day the issue hit the stands, let's at least try to be accurate about it, huh?