Sizzles do not have any genes for blue eggs, no. Neither do most Frizzles - you seem to use Sizzle and Frizzle interchangeably but they are not the same thing. Sizzles are a variety of Silkie with a different feather type. Frizzles are not a breed unto themselves except in the UK (Australia as well, I think). Frizzling is a feather type that can occur in any breed.
Sizzles will only lay varying shades of tinted/cream. Most commonly Frizzled breeds will not lay blue or green either. Typically, it is Easter Eggers which produce colored eggs, or less commonly Amerauanas, Legbars, or hybrids thereof.
Either that bird is some form of colored-egg layer frizzle or hybrid, or it did not lay that egg.