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It's a well known result that one time pads are provably secure. (Also, no PRNGs are involved.)

The PRNG is certainly involved in the generation of the one-time pad. You could tell if they used the ascii text of hamlet.

Could be actual random data is used, rather than a PRNG

Using a PRNG to generate an OTP is called a stream cipher, and then it isn't an OTP. :)

When using an OTP, you have to use non-pseudorandom values to avoid just being a stream cipher. If you're doing that, you can skip sharing the pad and just share the initial state of the PRNG.

If you go to the trouble of sharing the pad, go to the trouble of using random data within it. :)

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