Perfect pitch without relative pitch may by possible in theory, but not in practice.
Possible in theory means that, for example, a very young child may instinctively possess perfect pitch, but have not been exposed to music, and therefore have no sense of scales, melodies, etc. Or you may imagine an adult with similar talents -- inborn perfect pitch -- but who has lived all their life in a society where music doesn't exist. Under such circumstances you may say they have perfect pitch but zero relative pitch.
In practice, however, anyone who lives in our society is highly exposed to music, scales, and melodies, and as soon as these organized sounds start to hit your sense of hearing, relative pitch is automatically awakened and stimulated to grow.
Now, not all have an educated relative pitch, i.e. not all can name intervals and transcribe music by ear, but everyone, even non-musicians, can tell, for example, if you are playing a major scale from bottom to top or top to bottom. This means everyone have relative pitch in raw form. Without relative pitch you wouldn't be able to even tell that a melody is going up instead of going down, and everyone can tell that.
And not only that, but even non-musicians can tell, for example, is someone is singing a little out of tune. Detune one string of your guitar by 20 cents and play it -- even a non musician will know that something is wrong. Play an Arab scale (i.e. which doesn't use tempered tuning) to a non musician who has only been exposed to Western music, and they will instantly know that something is "wrong" there! All of that proves that even non-musicians have in fact a rather fine, micro-tonal sense of relative pitch, simply from hearing music in the background often enough.
And if that's true of non-musicians, in the case of musicians, even if one never deliberately did any form of ear training, it would be impossible to end up with complete ignorance of those intervals and melodic structures that are the building blocks of everything you do.
Bottom line, just being exposed to any music that is based on any systematic intervals structure (as opposed to, say, singing of birds or pitch changes in human voices) inevitably results in your brain internalizing that system of intervals to a rather precise and deep level. And that's why I submit that perfect pitch without relative pitch may exist in theory, but never in practice.