Here are my results for a couple of samples
The 3 number % are the chance to hit a stationary npc in the head with Maria, Mysterious Magnum, and Sniper Rifle in that order.

no FastShot with sniper 42% 32% 51%
no FastShot no Sniper 34% 28% 41%
with FastShot no sniper 29% 23% 34%
with FastShot with sniper 29% 23% 34%

I don't know what to say, numbers speak for them self. I did mention it was properly working on my other character (who picked trigger disc) but after using console commands to remove trigger disc & add fast shot and test it w. sniper,command, & gunslinger the perks were working as they were intended.
However on this character i can't seem to get any results from any of the perks if the character has FastShot. Go figure.

I also think the perks are glitched. The chances to hit my enemies in VATS is almost always low from mid-range. I don't know if they just nerfed the cammando, gun slinger & sniper perk like they did with most other perks but I see a big difference compared to FO3.

I just got done beating New Vegas and did every quest I could on my first play through, and while looking around for mods I found this post... I have to say I tried Vats maybe 3-5 times?? and then never used it again because how bad it was implemented into the game.
I also read the posts and comments about the Shotguns being broken in Vats and not doing the correct crit damage.

Just to add my experience, I have fast shot and I am getting sniper to work, but gunslinger and commando are both broken. I'll try to remove fast shot and see what happens.

My bigger issue is a problem with hitting the torso in VATS. Whenever I get a little VATS lag, the chance is almost cut in half.

Console user here. I was doing some... "testing" at NCRCF, and it works fine for me so far.

So can we say with certainty that this bug does in fact not exist?

Nope its still bugged for me, on the 360...

I hope you did about mabye 15 tests. I don't think the Numbers go up but the chances of hitting them do. Also it may only work on actual enemies. Non-friendlies.

Second. Even if it was a background change of 1% hit chance and 88% hit chance and the 88 missed and the 1% hit. Well thats how odds work. Just because 7 on 2 dice has a higher chance then rolling a 2 on 2 dice does not mean you won't get 2 snake eyes in a row or going 10 rolls without a 7 and 1 snake eye.

There's definitely an issue with shotguns in VATS. Plus, although the damage is given on the weapon descriptor menu as damage per pellet, I'm yet to see less than all the pellets either hit or miss.

I would also suggest from my experience that there are issues with the other perks mentioned, I've had some very odd VATS experiences.

Gunslinger and Commando are useless but I'm not surprised if there is bugs with the perks