The issue isn't that the data is public. The issue is the extraction of underlying behavior based on the spatial and temporal characteristics of the data being posted. E.g. the fact that I updated my profile on LinkedIn is not in question. But the underlying behavior is that the average user normally updates their profile around the time that they start a job-search. While this isn't true for every user, the use of an algorithm may turn up false positives, which may have unintended results, especially when this data is presented to your manager.
Secondly, while the updated profile is public knowledge, the temporal characteristics of the update isn't a feature that is directly published by LinkedIn. Call it a product feature; it is tailored to present the qualifications of a user, not to advertise the fact that they may be looking for a job. While one can argue that update is public knowledge, and must therefore be available for data-mining purposes, there is a subtle, but potentially dangerous leak of information here that is open to interpretation.
LinkedIn's position, that this leak may be potentially harmful to its users, and by extension, its core business, is therefore a fair point.