Eulerian Path In Directed Graph using SCC

Question

I read in geeks for geeks that we need to find out two things to know whether a digraph has eulerian circuit or not, they are:
1. All vertices must belong to a single SCC.
2. In and out degrees of each vertex should be the same.
My doubt is that why do we even need to find step 1, I am able to do it using only step 2 only, given the graph has only one connected component. Please help.
GeeksForGeeks

Answer 1

Here Alex Ravsky gives a link to a proof (pages 5-8) and indeed it says:

"Let G be a directed and weakly connected graph. Then: G Eulerian"

The fact that all vertices must belong to a single SCC isn't wrong of course, but it's nonsensical to include it imo as it follows from the following two conditions:

1. All vertices must belong to a single WCC.
2. In and out degrees of each vertex should be the same.