I mean that you can take the same traffic, using random assignment, and assign it into multiple A/B tests at once. Sure, there may be interaction effects, but they are random and statistically your evaluation of each test is unaffected by the others.
You need to be careful if you believe that there is reason to believe that tests will interact. For instance if you're testing different font colors, and different background colors, the possibility of red text on a red background would be unfair to both tests. But in general if you avoid the obvious stuff, you can do things in parallel. (If you have enough traffic you can analyze for interaction effects, but don't plan on doing that unless you know that you have enough traffic to actually follow the plan.)
Re-reading, I realize that I was as clear as mud here about interaction vs interaction.
The first paragraph is talking about random interaction. So, for instance, version A of test 1 was really good, and version B of test 2 got more A's from test 1 than version A of test 2 did. This gives version B a random boost. As long as things are random, it is OK to completely ignore this type of random interaction from the fact that you are running multiple tests on the same traffic.
The second paragraph is talking about non-random interactions. People who are in version A of test 1 and also in version B of test 2 get a horrible interaction that hurts both of those. If you have reason to believe that you have causal interactions like this, you can't ignore it but have to think things through carefully.
You need to be careful if you believe that there is reason to believe that tests will interact. For instance if you're testing different font colors, and different background colors, the possibility of red text on a red background would be unfair to both tests. But in general if you avoid the obvious stuff, you can do things in parallel. (If you have enough traffic you can analyze for interaction effects, but don't plan on doing that unless you know that you have enough traffic to actually follow the plan.)