I think a lot of this is very true. Stats are one thing, but most people applying to programs in I/O like Michigan State and Penn State are going to have great stats. In the end, it comes down to fit. Research fit with the faculty (1-2 matches per program is fine), your career goals' fit with the program's orientation (academic? practitioner? A balanced approach?), who else is applying that year, some demonstration that you know what you're getting yourself involved with (both in terms of I/O and research in general. Most programs know I/O experience and courses aren't available, but make sure you're letting them know that you're educating yourself with textbooks and some top I/O-OB-Management journals). If you haven't finished your year of RA or your thesis, make sure you still mention that you're doing it.
It all depends and it varies widely by program. You may not get into a "top program", not everyone does, but that may not matter. I think as you begin thinking about applying, my advice would be to focus less on "get into top program!!1~1!" and spend more time figuring out which programs are a match with you and your goals. Where are the faculty that match interests with you? Do you want a program that's purely academic in focus or do you want more of a scientist/practitioner balance? Is the program a match with your mentorship needs/what kind of mentoring model do they use (do you belong to one faculty or the whole department? Some places won't allow you to work with more than one person, others require that you do so)? Who would be able to offer you solid funding based on historical trends? Once you're in, also ask: is the program a fit culturally? If you are not hyper-competitive, stay away from a competitive environment and find one that is more collaborative/supportive. And again, who is offering the best funding? Funding maybe "shouldn't" be the end-all, be-all but it is a huge factor for most of us.
Also, just be aware - you may not get in the first time you apply. Or maybe you'll only get into a program you realize you aren't as excited about as you thought. That's okay. Try again in another year, it's not the giant failure some people make it out to be. Sometimes a small break is a blessing you didn't know you needed. ALWAYS strive to success - but be cool with needing to try again. I forget who said it, but seriously, the key to success is a high tolerance for failure.
If you want to apply to a top program? GO FOR IT. I'm an advocate of attempts. My stats and background are quite different from yours, but I will say that the places I got accepted to were "better ranked" places than where I was rejected... and -surprise- the fit was better at the top places. You never know how the dice are going to fall. It truly is a crapshoot.
If you have more questions, feel free to PM me. For what it's worth, your stats background will probably be attractive. The biggest issue is lack of research experience, so learn as much as you can in the mean time and emphasize what you have already done/are doing in your personal statements.