PhiloNibbler, take a look at this reference from my RATE analysis paper:  R.E. Taylor and J.R. Southon, “Use of Natural Diamonds to Monitor 14C AMS Instrument Backgrounds,” Nuclear Instruments and Methods in Physics Research B259 (2007) 282-287.
Taylor and Southon present a nice categorization of the different possible sources of contamination and background. Making measurements with an empty aluminum sample holder or with the ion source closed off from the rest of the system will allow characterization of SOME, but not ALL of the background. These measurements will give only a lower limit.
In the real world, there will be a number of other contributions, specifically: 1) there will be some false counts of radiocarbon when large amounts of C-12 and C-13 are present. This will depend on the specific details of the accelerator system, but is usually due to imperfect separation either in the accelerator or in the particle detector at the end of the system. Some of the C-12 or C-13 ends up being wrongly counted as C-14. 2) there will be cross-contamination in the ion source from previous samples ("ion source memory") and from atmospheric CO2. This is what Taylor and Southon were trying to study in the paper above. CO2 likes to stick to surfaces, and they theorized and showed that this would be lessened with diamond, which is hydrophilic. 3) there is always a small amount of modern carbon present in a sample due to the chemical procedures used to prepare the sample. This is why natural graphite usually gives the lowest (oldest) readings; it can simply be cleaned mechanically and pressed into a sample holder without the normal chemistry.
Because of these and other background mechanisms, measurements with a blank sample holder are NOT reflective of the true background of an AMS system.
"Science without religion is lame, religion without science is blind." – Albert Einstein
“I am very astonished that the scientific picture of the real world around me is very deficient. It gives us a lot of factual information, puts all of our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously.” – Erwin Schroedinger