I believe that Natalie Dessay started off training as an actress, and it shows in her performances. She retired from singing opera, but still performs in other venues both acting and singing.
When I was singing a lot of opera, my opera coach, who's at the Met, was the son of a well-known Broadway musical director and producer. So he knows the difference between musicals and opera performance, even though he concentrates much more on opera. When I first brought in some musical theater stuff to him, he said "You've really got the style right!". Later, when I had been singing a lot of musical theater and had been cast in another opera for him to coach me in, he had me add back vibrato and ground myself more for projection's sake to get back into the different vocal production and style that was right for opera. They have their similarities, but you're right -- someone singing "eeeef" instead of "if" just sounds wrong and artificial in musical theater, unless you intend your character to be that way.