Sure, you can cite many examples of companies that were in the right place at the right time (Yahoo, Google), or are examples from the time I was referring to (MS, Apple).
Right place at the right time is precisely one (if not the) formula to success, so I don't understand why you're discounting that. Yahoo! and later Google would not have been successful if the web wasn't so big that we couldn't easily find what we wanted. Microsoft being picked by IBM to build PC-DOS is the stuff of lore, and Apple ][ certainly was a right-place-right-time product.
There is even the chance that, even today, you can beat the odds and turn a small company into a success, but it's certainly not as likely as it once was.
I don't really know what numbers we might use to prove the comparison you want to make, but I don't think it was more likely back in the day. Apple's early competitors included Atari, Commodore, and many others who ultimately didn't make it. Microsoft fought Lotus and WordPerfect and GEM and others. Success was not at all likely, much less guaranteed. Do you know of Stacker? Stac had a clever disk compression product, Microsoft killed them. Netscape had the first good web browser, Microsoft killed them. Apple killed a number of third party apps, not to mention the clones. This is a bloody, bloody path if you care to look back.
The problem is that it's incredibly hard in today's environment to survive as a small business, much less flourish. If you achieve any success at all, you'll attract the attention of larger companies who will either buy you out (a good outcome from your perspective, maybe not so good for the industry) or use their much deeper pockets to try and put you out of business through lost-leader pricing or outright anti-competitive practices.
Apple and Microsoft both had to contend with IBM, in an era where nobody was ever fired for buying IBM. I don't see how that was any easier.
Behemoths generally have groups of analysts whose sole raison d'être is to seek out new lines of business. If anything new appears on the horizon and looks like it will generate revenues, these organizations are quick to jump in, buy out or push out any competitors, or even quash new technologies if they feel it may compromise the profitability of existing revenue streams.
Again, I disagree. Behemoths indeed have certain advantages, but quickness is almost never one of them. Microsoft was late to music players, and late (or too early, if you want to take that perspective) to the modern smart phone and tablets, and not particularly early in game consoles. IBM was late enough to personal computers that Apple got itself a foothold, and late enough to PC operating systems that DOS and Windows survived. You can easily look at Android to pick out a number of features that Apple was or is late at. Google itself was playing catch-up in things like web mail, and of course phone and tablet OS.
It all adds up to an environment that heavily favors large corporations at the expense of small businesses. This is not news and I find it hard to fathom that anyone can honestly feel that is not the case.
I'm not arguing that this is not the case, I'm arguing that this is not a new case. I'm saying that small companies have always had a very tough time, especially when they tread into areas that big companies become interested in. In fact, it was far worse back then when we didn't even have anti-trust laws.
Now, I do agree with you that many start-ups seem to be primarily interested in getting bought than building itself into a big company, but how much of that is just wanting the quick buck and not willing to put in the real work ("kids these days"), and how much is your thesis that it's not possible anymore? Facebook, for example, doesn't seem that interested in being bought out.