It is pretty certain that Janis met John, but not much is documented. The birthday thing was a cassette that a bunch of people who recorded at the Sunset Sound got together there to make him a birthday tape. Janis was recording Pearl there already, so just added her song, but the tape is her, Donovan, Blossom Dearie, Ringo, George and others. As far as I know, Yoko still has it, and no one except those that had recorded it knew about it. She found it going through John's stuff after he died, and when they approached her later to do a special on him, it was on a radio special called the Lost Lennon Tapes. Up till then no one really knew about it. It was her insisting that they release it.
When John got the tape, he had just heard about Janis' death 2 days before. I think it kinda bothered him. It spooked John that Janis had sent this for his 30th birthday and was dead when he got it. He had told Yoko that it made him think he could be gone just like that, too, and 10 years later at 40, he was.