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This is correct assuming the applicant serves the correct certificate as part of the Planning Application.
@Adlopa post suggests that the incorrect boundary line was shown on the planning drawings suggesting the incorrect certificate was completed. This is important for the classification of the proposed wall and one for the party wall surveyors to agree as part of the award.
@Adlopa post also suggests that a Thames Water build-over application might be needed and worth asking your soon-to-be-appointed party wall surveyor to check.
Planning permission isn't even linked to ownership of the land. You could apply for planning permission for the neighbour's garden if you wanted.