I don't think this is correct. But the terms are tricky, so let me rephrase your question with precise info:
"If it is too dark to shoot with a 1/60 shutter speed at 30 FPS, should I maintain that shutter speed, and decrease my frame rate (to 24 FPS, 15 FPS, or 10 FPS)?
The answer to that question is "no". You should choose your frame rate; 30 FPS is common, and 24 FPS is considered "cinematic". But you should never go lower than that.
So you have selected 30 FPS, and the ideal shutter speed is 1/60. If that is too dark, should you slow down the shutter to 1/50 or even 1/30? The answer to that question is usually "yes". Like most rules, the 180-degree rule is more of a suggestion for what works best in most cases. But in dark areas, it's OK to slow the shutter speed. And in bright areas, it's OK to increase the shutter speed.
But what about when it's really dark? Can you continue to lower the shutter speed to 1/10, 1/5, or 1/4 of a second? The answer to that question is "absolutely not", because then you won't be able to fit 30 frames/second. The slowest shutter speed for 30 FPS is 1/30; you can't go any lower.
So what do you do? Increase the ISO sensitivity. If you are on auto-ISO, this will be done for you. But if you are in manual, you will have to do it yourself. A doubling of the ISO sensitivity (e.g., from 400 to 800) is equivalent to a halving of the shutter speed (e.g., from 1/60 to 1/30).
Now what about when it's way too bright? You want 30 FPS, and you want 1/60, so you have to lower the ISO sensitivity. But what happens when you hit the lower limit? You have two choices there: 1) increase the shutter speed (to 1/125, 1/200, etc.) or 2) add a neutral-density filter. If you increase the shutter speed too high, you can get some choppy motion. And right now, the ND filter options for this camera are limited.