Firstly, the etymology of the word "culture" is based on an agricultural metaphor. It refers to "cultivation of the mind". It makes no mention of social transmission. I propose that individual learning may also be used to "cultivate the mind".
Then there's the issue of what is important about culture:
Brains allow organisms to use their brains to adapt to the environment. Organisms use both social and individual learning to help them do that. However, social learning additionally allows groups of organisms to maintain knowledge pools for long periods of time - allowing for cumulative cultural evolution. This possibility seems to be the main phenomenon that makes culture of interest. However, now there are other means of creating persistent databases - by creating backups. The possibility of making backups creates potentially-immortal learning systems which can preserve large databases without the need for separate individuals to act as peers. Such systems could exhibit cumulative cultural evolution using individual learning only.
Also, we currenly lack a good term for "learned material". "Culture" is material that is learned socially. The term "knowledge" excludes learned behaviour patterns. The term "skill" excludes learned knowledge. The term "engrams" only refers to how learned material is stored. "Learning" seems pretty overloaded. Overall, there seems to be no good general term for "things that have been learned".
These considerations suggest that it would be better - scientifically speaking - if the term "culture" was defined so that it includes individual learning.
I don't think is is tremendously important to have a term for social learning that excludes individual learning - since social learning and individual learning are such inextricably interconnected phenomena - however, if such a term is needed, "transmitted culture" could be used.
Of course, "culture" is a common word with considerable inertia. It seems appropriate to hesitate before attempting to assign it a counter-intuitive scientific meaning. Redefining common English terms is a reliable way to self-identify as a crank. However, expanding the term "culture" so would resolve some boundary problems with both cultural evolution and memetics. I think that we should bear this option in mind.