I've never heard of it, but after two minutes of looking at Google hits, here is my suspicion:
1) Your Web hosting provider actually is a sales organization, and the hosting backend service is provided by Alabanza (a high-volume Web hosting wholesaler). You can check this by doing an ARIN lookup of your IP address to see who actually owns it. For example:
OrgName: Alabanza, Inc.
OrgID: ALAB
Address: 10 East Baltimore St., 10th floor
City: Baltimore
StateProv: MD
PostalCode: 21202
Country: US
NetRange: 216.147.0.0 - 216.147.127.255
CIDR: 216.147.0.0/17
NetName: ALABANZA-BALT-2
NetHandle: NET-216-147-0-0-1
Parent: NET-216-0-0-0-0
NetType: Direct Allocation
NameServer: NS.ALABANZA.COM
NameServer: NS2.ALABANZA.COM
Comment: ADDRESSES WITHIN THIS BLOCK ARE NON-PORTABLE
RegDate: 1998-12-17
Updated: 2000-01-26
2) mod_rewrit seems to be something that Alabanza uses internally and it is not intended to provide an interface for end users. "For security reasons" they won't talk about it.
3) mod_rewrite (the real one) is not available to you.