> He got personal visits from both Ballmer and Gates that pressured him to stay with Microsoft[2] but did not balk.

So he did not refuse to comply, i.e. complied? I think the parent is right: Grandparent probably meant "he did not budge".

Per Merriam-Webster, 'to balk' means:

1: to refuse abruptly

2: to stop short and refuse to proceed

Per Cambridge Dictionary, it means:

to be unwilling to do something or to allow something to happen

So "He did not balk" can be read as "He did not stop" / "He was willing to let things proceed"

> Per Cambridge Dictionary, it means: to be unwilling to do something

You agree balking means being unwilling, right?

So not balking means being willing, right?

He did not balk, therefore he was not unwilling, therefore he was willing, right?

So he was willing to do what Microsoft asked, "but" so was the next guy? What?

> So he was willing to do what Microsoft asked?

No. Balk = stop and return on your steps. He was moving towards ”migrating more than 14000 PCs in public administration to Linux”, Gates and Ballmer tried to make him stop, but he continued on his path.

> So not balking means being willing, right?

In this case, willing to proceed with what he was planning to do, that is, moving from Windows to Linux against Microsoft's wishes.

edit: And you're right that this implies "balking at Microsoft's proposal". Personally, I did read the sentence as intended ("they wanted him to balk (= stop his plans), but he did not"), but I can see how the phrasing can be misleading...