I will make the wild assumption that ShellCheck is just checking the printf utility format string operand (and perhaps checking that there are enough operands supplied to match %format-specifier and * in %*.*format-specifier occurrences in the format string operand). Since a format string can be reused if more operands are present than format specifiers, it would be a lot harder for it to determine when an unquoted shell variable is expanded in an operand is wrong versus when an unquoted shell variable in a format string could cause early termination of the format string.
No. There is nothing wrong with this this printf command (other than the fact that it won't do what you want on a machine using an EBCDIC codeset and will only work on certain output devices that understand the escape sequence you have encoded at the start of that output). There are no variables in that format string that could be expanded to require additional operands. That command (with double-quotes as you used them or with the double-quotes replaced by single-quotes) produces a partial line of output that is perfectly well-formed. And, since that format string operand contains no percent sign characters, the following commands would also be valid commands producing exactly the same output (more slowly):

Code:

printf '%s' '\x1B[0;34;43mIs this a valid posix compliant line?'
printf '%s' '\x1B[0;34;43mIs this a valid posix compliant line?'

(and, in both of those commands the 1st two single-quotes can be changed to double-quotes and the last two single-quotes can be changed to double-quotes with no difference in the output (but it will run slightly more slowly)).