For some random and arbitrary reason you and this existing employee didn't get on and are likely not to work well together.
This fact is obvious to them, to you and even HR - everyone is in agreement on this.
I wouldn't look as the rejection as just personal criticism of you - I'd see it as rejection of a team consisting of you and them. Unfortunately as they're the current employee and you're the applicant, you get the shitty end of this 'team rejection stick'.
I'd take the suggestion to "apply to other teams" as strong positive feedback and do just as they suggest. I'm sure Twitter has a long and illutrious applicant list, so if they didn't think you were a fit for the company they could have just told you (or not) and phoned the next person.