Hi-Fi had nothing to do with RCA outputs. You may be thinking of S-video, which was separate luma and chroma signals available from Super Beta and Super VHS decks (and, years earlier, from Atari and Commodore computers). On a side note, LaserDisc did not offer it because those components were mixed on the disc and there was no point in providing discrete outputs for each.
And no, they did not break the tape formats. Beta Hi-Fi came out in the early '80s and VHS Hi-Fi followed a couple years later. From Wikipedia:
"Around 1984, JVC added Hi-Fi audio to VHS (model HR-D725U, in response to Betamax's introduction of Beta Hi-Fi.) Both VHS Hi-Fi and Betamax Hi-Fi delivered flat full-range frequency response (20 Hz to 20 kHz), excellent 70 dB signal-to-noise ratio (in consumer space, second only to the compact disc), dynamic range of 90 dB, and professional audio-grade channel separation (more than 70 dB). VHS Hi-Fi audio is achieved by using audio frequency modulation (AFM), modulating the two stereo channels (L, R) on two different frequency-modulated carriers and embedding the combined modulated audio signal pair into the video signal. To avoid crosstalk and interference from the primary video carrier, VHS's implementation of AFM relied on a form of magnetic recording called depth multiplexing. The modulated audio carrier pair was placed in the hitherto-unused frequency range between the luminance and the color carrier (below 1.6 MHz), and recorded first. Subsequently, the video head erases and re-records the video signal (combined luminance and color signal) over the same tape surface, but the video signal's higher center frequency results in a shallower magnetization of the tape, allowing both the video and residual AFM audio signal to coexist on tape."
I sold a decent number of HR-D725s where I worked in high school. You see very few products with its build quality today. I still have the original JVC promo tape that showcased the release of VHS Hi-Fi, featuring a voiceover by Don Adams (Get Smart).
