Other people think that if someone is a good wrestler, they'll kill everyone on the mat in judo.
They're wrong, too.
Some people think that jiu-jitsu players will beat judo players on the mat.
They're often wrong.
Other people think that most judo players suck at matwork.
They're right, but it doesn't mean that jiu-jitsu players and wrestlers will necessarily beat them.
I can't believe I have to explain this to you --- jiu-jitsu, judo and wrestling all have different rules. The MAJOR difference in matwork is in judo you get very little time to score with your technique, where BJJ and wrestling referees will let you hang around on the mat all day.
That's just the way it is. It's like in football where five guys can jump on one quarterback and knock the guy down and that's not cheating but if you step over a line it's a penalty. Those are the rules and don't whine about it.
This does have some implications for cross-training. If you are a judo player training at BJJ it may not help you as much as you expect on your offense because they often take longer to set up than will be allowed in a judo match. Also, there are a lot of restrictions in judo - and they vary from one tournament to the next. In some, only brown belts can do armbars, in others only black belts. Young kids are never allowed to do armbars at judo tournaments.
On the other hand, if you are a judo player cross-training in BJJ your defense should get better because they get a LOT longer on the mat. You won't be able to save yourself by waiting for the referee to stand you back up. Also, if you are AWARE of the differences, you really can get a lot out of BJJ because they do spend a lot more time on the mat and, consequently, have a lot better defense for matwork (because they need it) and may have some entries into armbars you haven't seen before.
Admittedly, I've been in judo a LONG time .... but I've never seen anyone in BJJ do an armbar I hadn't seen. I mean, let's face it, there are only so many ways you can twist an arm. I have, on the other hand, learned new entries, new escapes and new drills.
Does wrestling make you brain-dead? Seriously, I'm asking because I've seen some very good judo players who were also very good wrestlers that, when they competed in judo, never did so much as a half-nelson. They'd do their standing technique, like a double-leg takedown, which is now illegal in judo, but perfectly legal wrestling moves on the mat, they never did. When I would ask them about it afterward they would say,
"I don't know. I guess I just never thought about it."
I am embarrassed to admit that I would have known the answer if I had only listened to myself talk during practice,
"You'll do in tournaments what you practice. In the middle of a match is one hell of a time to be figuring out what you want to do next in this situation."
If you don't practice doing a half-nelson or a sit-out in judo practice AS A TRANSITION FROM YOUR STANDING JUDO TECHNIQUES you're much less likely to do it in a tournament.
Judo matwork techniques CAN be lethal if a person gets really good at them, and judging an individual based on the stereotype of a sport is always a bad thing.
When Ronda first started in mixed martial arts, a lot of women in jiu-jitsu and wrestling made comments like,
"She may be an Olympic and world medalist in judo and have some good throws, but I have a game plan. I'm just going to the mat with her."
To which I, Blinky, Gary Butts and the other coaches at matches would always reply,
"Yeah, that sounds like a really good strategy, You should go with that."