Yes, the calculator is correct, but theory is always different from practice. As it shows, there is a 'nominal thickness' which is thicker and (somewhat) accounts for irregularities. It should be kept in mind that this is the minimum thickness required before bursting. Often people will test something at a pressure that is 150% higher than operating pressure.
In practice, things tend to weaken with time, and experience jolts and scratches etc, and always have imperfections, and so engineers multiply the minimum amount by a factor for safety. This is especially troublesome for carbon fiber because there can be air bubbles and many irregularities. Metals however, are very uniform. How can you accurately determine a good factor to multiply when you don't know the weakest irregularity? It is only as strong as its weakest point. It brings up problems with statistics that Nassim Taleb talks about in books like The Black Swan. How can you account for the unknown? If you could scan the material and find irregularities, then it may be possible to estimate the weakest point and either fix it or apply a better factor.
I wouldn't worry about epoxy weakening it. It is a composite, like rebar reinforced concrete, with benefits from both, not a simple average.
https://www.matweb.com/search/datasheet_print.aspx?matguid=39e40851fc164b6c9bda29d798bf3726
Here, it shows the Ultimate Tensile Strength for carbon fiber/epoxy. It includes both, not just the carbon fiber. It gives a range of 1GPa - 3.8GPa.
You can do a literature search for experimentally measured values. This one for instance is 1GPa, so I would use that value to be safe. The value depends on how well it is made.
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.e3s-conferences.org/articles/e3sconf/pdf/2017/07/e3sconf_eems2017_03018.pdf
Carbon Fiber really does have an amazing set of properties and it will continue to gain in popularity, as its method of production continues to improve. Understanding the caveats is an ongoing challenge and is actively being researched.
My PhD in chemistry involved TEM and dealt with defects. Defects are the things which keep us up at night. People use vacuums and injection moldings at high pressure to decrease bubbles, but there will always be some irregularity, and because of randomness, there's a chance they could all happen to be in one spot. It's not a concern if it is on the hood of a car, but it is catastrophic under pressure. There's no simple calculator for it, so it is wise of you to be skeptical of any calculator!