Valid use of the keyword mutable?

Ah hello.

I would like opinions on the use of the keyword mutable, and whether or not how I have used it, described below, is valid.  Please consider the pseudo code below:

class CStore
{
public:
	CObject* GetObject(const std::string& strName)
	{
		SortAlphabetically();
		
		// Retrieve item "strName" using lower_bound() or equivalent
	}
	void SortAlphabetically()
	{
		// Sorts m_storage alphabetically
	}

private:
	std::vector<CObject*> m_storage;
};

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OK.  I had code similar to the above, and was looking to tidy it up.  I had the brainwave that GetObject() should be const; after all, it does not modify the object in any way.  I then had to make SortAlphabetically() const for obvious reasons.

This lead to a problem.  GetObject() should be const; but should SortAlphabetically() really also be const?  I did some reading and found out about "logical constness" vs "bitwise constness", and realised that SortAlphabetically() could be made const as although it does change the bit-pattern of the CStore object, it would not change the way the object appears to clients (so hence remains logically const).

Feeling appeased, the final piece of the solution was to make m_storage mutable, which I did, then happily continued pounding my keyboard writing new code.

For a short while.

A little nag came into my mind; having made m_storage mutable, what was to stop somebody modifying my class and writing a new function like this:

void CStore::DoNothingSpecial() const
{
	m_storage.clear();
}

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Eeek!  Because m_storage is mutable it can be adjusted in whatever way required, so client code could call this function assuming nothing about the CStore object will change, but in reality after the call to DoNothingSpecial() it is completely different to before the call.

Am I right to be concerned with the above, or is it assumed that the anyone modifying the class will not do (stupid) things like this?

How would you get around this issue?

TIA