I would bet that what happened was worse than plagiarism or borrowing. An alternative:
1. Group A submits a proposal.
2. Somebody on the evaluation team is "friendly" with Group B.
3. That evaluator votes to reject the proposal from Group A
and sends a copy to Group B.
4. Group B submits a very similar proposal, which is accepted.
Another kind of plagiarism that a colleague and I encountered:
1. We gave a talk about something we called X.
2. A member of the audience came up afterwards to ask some
questions about X.
3. A couple of years later, we noticed that he had published
a paper about something for which he used the same name X.
But he did not acknowledge us or any of our publications.
4. He even submitted a patent application for his version of X.
But the so-called "invention" he described and his claims for it
had only superficial similarities to our version of X.
5. We didn't bother to challenge the patent application. Instead,
we just renamed our version Y and trademarked the name Y.