Cisco :: 3750 Via Vlan250 From Core 6509 - Getting Connection Refused?

We just replaced our ancient 6509 dedicated SAN switch with a Nexus 5548UP (with 4 2248 FEXs).Our old SAN 6509 was completely separated from the Core 6509, and that Core 6509 doubled as a Datacenter switch. We've now segmented the "Datacenter" and "Core." The SAN and servers are connected to the Nexus gear rather than the Core. The old SAN had only 3 vlans. One for SAN data (Vlan16), one for management interfaces (Vlan250), and one for switch management (Vlan15).

As part of my cleanup, I want to get rid of that Vlan15 and use vlan250 for switch management. In another building, we have a 3750 that provides SAN (Vlan16) and management (Vlan250) connectivity to a single Equallogic box and a Dell PowerVault tape drive for backup purpose. That 3750 is the only device that still has an address on Vlan15 (other than the core). Refer to the drawing below.

The Core 6509 is the gateway for Vlan250 and Vlan15. I have created an interface for Vlan250 on the 3750. ACLs exist on vty connections of each switch allowing telnet access ONLY from the Mgmt 2960. There are no ACLs on the Vlans themselves.From the Mgmt 2960, I can telnet to the 3750 using either its Vlan250 IP address or its Vlan15 IP address. However, if I shut down Interface Vlan15 on the Core 6509, I can no longer telnet to the 3750, not even using its Vlan250 IP address.

The connection times out. If I attempt to telnet to the 3750 via Vlan250 from the Core 6509, I get connection refused (which I should get due to the ACL on the vty connections). I can still telnet to other devices on Vlan250 (such as the management interfaces on the Nexus 5Ks). Why am I able to telnet to the 3750's Vlan250 Interface only when the Core's Vlan15 Interface is Up?