us = inch.com
them = ctonline.net

First, I do an nslookup from one of the root nameservers, with 
query type = A:

> server G.ROOT-SERVERS.NET
Default Server:  G.ROOT-SERVERS.NET
Addresses:  192.112.36.4, 192.112.36.0

[Now I input one of your dialup ips:]

> 207.16.240.45
Server:  G.ROOT-SERVERS.NET
Addresses:  192.112.36.4, 192.112.36.0

Authoritative answers can be found from:
16.207.in-addr.arpa     nameserver = AUTH00.NS.UU.NET
16.207.in-addr.arpa     nameserver = AUTH50.NS.UU.NET
AUTH00.NS.UU.NET        internet address = 198.6.1.65
AUTH50.NS.UU.NET        internet address = 198.6.1.161
*** No address (A) records available for 207.16.240.45

[Ok so far.  Now I try to get the answer from uunet, who is authoritative
for the 16.207.in-addr.arpa zone:]

> server AUTH00.NS.UU.NET
Default Server:  AUTH00.NS.UU.NET
Address:  198.6.1.65

> 207.16.240.45
Server:  AUTH00.NS.UU.NET
Address:  198.6.1.65

*** AUTH00.NS.UU.NET can't find 207.16.240.45: Non-existent host/domain

[Which would be the problem.  This would also explain why your localnet
looks ok, but the rest of the Internet can't get the reverse lookup.]

As a counterexample, take a look at what happens when I start from 
the root nameservers and query for one of our dialup ips:

------------------------- Begin included text -------------------------
> server G.ROOT-SERVERS.NET
Default Server:  G.ROOT-SERVERS.NET
Address:  192.112.36.4

> 206.138.209.1
Server:  G.ROOT-SERVERS.NET
Address:  192.112.36.4

Authoritative answers can be found from:
138.206.in-addr.arpa    nameserver = AUTH00.NS.UU.NET
138.206.in-addr.arpa    nameserver = AUTH01.NS.UU.NET
AUTH00.NS.UU.NET        internet address = 198.6.1.65
AUTH01.NS.UU.NET        internet address = 198.6.1.81
*** No address (A) records available for 206.138.209.1
> server AUTH00.NS.UU.NET
Default Server:  AUTH00.NS.UU.NET
Address:  198.6.1.65

> 206.138.209.1
Server:  AUTH00.NS.UU.NET
Address:  198.6.1.65

Authoritative answers can be found from:
209.138.206.IN-ADDR.ARPA        nameserver = NS.INCH.COM
209.138.206.IN-ADDR.ARPA        nameserver = NS2.INCH.COM
209.138.206.IN-ADDR.ARPA        nameserver = NS.UU.NET
NS.INCH.COM     internet address = 204.178.32.1
NS2.INCH.COM    internet address = 204.178.32.4
NS.UU.NET       internet address = 137.39.1.3
*** No address (A) records available for 206.138.209.1
> server NS.INCH.COM
Default Server:  NS.INCH.COM
Address:  204.178.32.1

> 206.138.209.1
Server:  NS.INCH.COM
Address:  204.178.32.1

Name:    port101.dialup.inch.com
Address:  206.138.209.1

> set all
Default Server:  NS.INCH.COM
Address:  204.178.32.1

Host:    port101.dialup.inch.com
Address:  206.138.209.1

Set options:
  nodebug         defname         search          recurse
  nod2            novc            noignoretc      port=53
  querytype=A     class=IN        timeout=5       retry=4
  root=a.root-servers.net.
  domain=com
  srchlist=com

> 

-------------------------- End included text --------------------------

World | Inch