Not true, sadly. In my experience there is a big element of luck, and the headline matters a lot.
For example, my most popular ever submission (1341 upvotes) didn't get a single upvote when I submitted 4 months earlier under a slightly different headline.
Well, yes and no. I’d say the new headline was very similar content, albeit pitched a bit differently. :)
I usually try not to repost, because I think it’s rightly frowned on, but I do have a few less extreme examples where the exact same post got to the front page a second time after sinking without trace the first. It seems kind of obvious that the timeline of the first few upvotes is critical, and somewhat random.
For example, my most popular ever submission (1341 upvotes) didn't get a single upvote when I submitted 4 months earlier under a slightly different headline.