I often wonder if that friendship though did more harm than good for Karen. I believe Olivia is just as warm and genuine as she comes across in interviews. I'm sure she cared for Karen. But the problem is that I think Olivia embodied much of what Karen wanted in her own life with regards to Olivia's looks, 1980's success, branching into movie's and confidence.
On top of that, Olivia got the role in Grease! Karen was performing numbers from Grease in the Carpenters stage act years before Olivia was in the movie. Karen was very much familiar with the play and later movie. I can't help but think that Karen must have had twinges of jealously seeing Olivia in the skin tight black leather outfit, red lipstick, high heels, and coiffed hair. Karen would simply never have been able to look like that. Though she wanted to I'm sure.
Karen was a beautiful woman no doubt. However, she wasn't considered a bombshell, drop dead gorgeous woman like Olivia. Olivia was a few inches taller than Karen and had the build that Karen desperately wanted. Karen was a bit hippy and had broad shoulders. Even in her emaciated state, if Karen was fully covered, if you didn't look at her face, she deceptively looked healthy. Her body had a certain build so her hips were a certain way. There was no amount of dieting that would get rid of her bone structure. Whereas Olivia had that twig-like figure. Combine that figure with her blonde hair (long or short) and she was really a strikingly beautiful woman. From the average American vantage point, Olivia was more the hot sex symbol than Karen.
Olivia in Grease!
Then Olivia's absolutely smash album 'Physical' came out shortly after Made In America (which was a comparative flop sales-wise). It was a completely different album than MIA. It was much more contemporary, had more of an edge. The title song spent 10 weeks at #1. Olivia had follow-up top-5 hits with 'Make a Move on Me' and 'Heart Attack' (the later ironically came out around the time of Karen's death in 1983). While Karen was in New York in therapy in 1982, A&M released 'Beechwood' which barely cracked the top 100. Meanwhile, Olivia was enjoying tremendous success and touring the world.
I think Karen's voice was better than Olivia's, more distinctive. But as I've said before, Karen was also ambitious and competitive. There was likely apart of her that was envious of Olivia's looks and success. On the man front, Olivia seemed to have more confidence. She didn't land the kind of man Karen was looking for. Olivia's boyfriend Matt Latanzi was 10 years Olivia's junior and not anywhere near as successful as she. He was a dancer in Xanadu. So Karen probably wasn't envious of all aspects of her life. Olivia was a year older than Karen and one of just a few friends near her age that wasn't married and with a child or expecting one. So this probably gave one common thread for her to bond with Olivia on. But I think that common attribute was overshadowed by envy for Olivia's looks and continued success.
Interestingly, Olivia's success also came to end later in 1984 after her last Top 5 hit 'Twist of Fate'. Success doesn't last forever for anyone. But the fact that Olivia was seeing this early 80's success and the Carpenters hadn't seen a Top 10 hit since 1975's 'Only Yesterday' must have been a tough pill for Karen to swallow. The early 80's saw a slew of adult contemporary acts scoring #1's like Air Supply and Christopher Cross. The Carpenters couldn't find the right song. 'Touch Me When We're Dancing' was gorgeous but not a bona fide Top 10.
At the end of the day, as nice as Olivia seems to be, I just don't think the friendship was healthy for Karen. I think it created some jealousy for her. I don't believe this had any significant factor in Karen's demise but I think it was something that did cause frustration and added to the the anorexic behaviors that eventually killed her.