Yes you understand it well.
Although all posts from leo, end up on Hive as well.
I'm seeing this post and replying to it from Peakd and Hive.blog, as they are general content frontends.
Posting on Leo is posting on Hive as well. The post is visible on all the generic Hive front ends. Just if you want to use the simple process that leo provides and stick with it, you will need to post from leo, and then everyone can read it or interact with it from Peakd.com or Hive.blog.
The idea behind the twitter sign up on Leo is to make the first step easier, and then as they get more into it, advance a bit, allow them to get their keys and become fully independent.
If you want full control at start there is no way around the keys and all that.
p.s :)
Once a user have a bit more than 5k Hive Power, he can claim and create Hive accounts by himself. Depending on the chain congestion, around 5k HP equals one Hive account per day.
You will find the option to claim and create accounts in the wallet section on Peakd.com, under the delegate option.
This means you can create the accounts for your students by yourself and give them the user names and the keys.