Yup.
http://www.st.com/content/ccc/resource/technical/document/application_note/c6/eb/5e/11/e3/69/43/eb/CD00221665.pdf/files/CD00221665.pdf/jcr:content/translations/en.CD00221665.pdfIn short, by putting a crystal between caps, you're using a transformation, which effectively turns it from a series resonant crystal to a parallel resonant filter. The impedance of that filter, and therefore the voltage needed to deliver some current, or the current required to develop some voltage, is approximately the reactance of those capacitors.
The crystal resonance is "pulled" or loaded by external capacitance, so it's only correct when the total capacitance, as seen by the crystal, equals the datasheet value. This includes pin capacitance (which isn't always well documented) and stray capacitance.
The oscillator is only as powerful as it is designed to be. The ST oscillators appear to be fixed gain, so you need a crystal that's high enough impedance (low enough CL) to work reliably. Others are designed with a full logic pin output, and you add an external resistor to set the drive current (it's usually on par with the resonator impedance: in the ballpark of ~1k for 10MHz crystals, ~50k for 32kHz, etc.). Some (I think most AVR and MSP430 do this) have software controlled options for drive strength / power / current consumption.
This should also give you some idea what kind of options there are, if you should wish to do something oddball, like use an LC resonator instead.
Tim