I recommend reading up on it: https://www.nature.com/articles/s41586-024-08025-4
But no, it only ever picks tokens that are in the probability distribution of the last layer, and it might have picked anyway.
The randomness properties of the PRNG will be very similar to other random number generators, it is just chosen to be vulnerable to a particular cryptanalytic attack (that requires a private key known only to anthropic). I think of it like the Dual_EC_DRGB generator rather than a biased coin.
I'm not entirely sure (haven't read the original synthID proposal), but I believe that the re-weighing is set to make both your scenarios and mine equally likely, averaging out to net Zero effect on quality.
> SynthID-Text can be configured to be non-distortionary (preserving text quality) or distortionary (improving watermark detectability at the cost of text quality).
To random words you pick and provide a sufficient amount of text to vary with random number without losing its meaning you need a text with high entropy.
Also, it would probably provide higher entropy to write normal human-sounding English instead of reusing a repetitive grab bag of load-bearing phrases. This theory doesn't really make any sense.