My only other explanation is: the 'Princess Royal wasn't an Inn, but a beer seller's establishment - of which there were many in the 19th century - BUT if that's the case where was the Rose and Crown on census 1891 and 1901? Seems odd don't you agree that the 'Princess Royal' can be found in 1891 and 1901, cannot be found in later census, but the Rose and Crown IS on the 1911 census, however the Princess Royal isn't!
Your call Stephen, we can merely help with evidence found, up to you to evaluate the evidence - but I know how I'd interpret it.