I am sure they meant that the output of a conditional expression would be an encrypted boolean.

A conditional branch would become an encrypted conditional branch. That means, you wouldn't be able to infer the branch from the encrypted output.

Let's take a simple example. I have an algorithm X which takes two integers and returns an integer.

Let's say I want to run this algorithm on a third-party VPS. I obfuscate the algorithm X, in order to hide the operations that X does. Let's called the obfuscated version OX.

I host the OX algorithm on the third-party server, and start supplying it pairs of integers. The third-party is observing the set of inputs and outputs:

  (4, 4) => 8
  (3, 2) => 5
  (1, 0) => 1

From these observations, the third-party would be able to infer what OX does. (simple addition in this case).

Now, however, if I use HE, I will get an algorithm (HX) which takes encrypted input and spits out encrypted output. A third-party will see the corresponding log of inputs and outputs like this:

  h3830120cjfakj, 102309123clals => 293sdlzlxdf
  94ka3lkc.zdkf, 102kksdllz => 1923939nddd

From these observations, it is impossible to know what HX does (as per the theory).