I think the OP was referring to data transfer bandwidth (the throughput, or data rate), rather than the traditional electronics use of "bandwidth" (referring to the width of the transmitted signal in the frequency spectrum; though "channel width" is a more exact term).
Of course higher carrier frequencies don't have a higher bandwidth, because bandwidth is a property of the whole system, including the data signal and modulation method. You can make the bandwidth as big or small as your system's constraints allow (e.g. one constraint might be to keep most of your transmitted power inside the allocated bandwidth).
If your data signal is modulated in the exact same manner regardless of the carrier, varying the frequency of the carrier will not affect the transmitted signal's bandwidth. The carrier frequency imposes the upper limit on the data signal's frequency, and thus a higher carrier frequency will theoretically allow for a high data rate.
Practically, however, the data signal is almost always much smaller than the carrier signal, and the transmitted frequency is subject to many other important factors such as noise, signal propagation through the environment, etc... In the case of 2.4GHz vs. 800MHz carrier frequencies, there is no practical gain in potential data rate.
This is all based on my limited understanding of communication theory. Please correct me and/or provide further details if possible!