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For QoS marking, or validation of existing markings, by-the-book you want to perform it as close to the source as possible, including, also if possible, having the source mark the traffic.
Also by-the-book, core and/or distribution layers only use markings for different service treatments and only change markings if bandwidth usage isn't within "contract". Edge device also use markings for different service treatments, but their analysis and possible manipulation of markings are often much more involved than core or distribution devices as edge devices are often a trust boundary. I.e. core and distribution often rely on the edge device to validate markings.
From what you've described, it's unclear why your senior engineer prefers to implement QoS marking on all layers unless you mean QoS marked treatment. The former would be unusual, the latter by-the-book.
As to your belief that you have sufficient bandwidth on a edge 3750 switch or 3750 stack so you only need to trust Avaya phone markings, perhaps that's true and perhaps not. Transient microbursts can cause transient service issues even when it appears you have sufficient bandwidth.
You mention your 3750 uplink is gig. Are the edge ports gig? If edge ports are FE, are there more than 10? In other words, is the uplink oversubscribed? If so, it can congest.
Conversely, if uplink is gig and edge ports are FE, than they can be oversubscribed on download.
On the same edge device, can more than one port transmit to another port at the same time?
The real truth is, by-the-book QoS, insures proper service level treatment anywhere within your network. However, by-the-book QoS can also be a headache to implement and maintain especially without some automation support. I'm guessing you're really asking what QoS is really needed where in your network.
Well, you only really need QoS where there's congestion that's adverse to your traffic's service needs. This can dramatically decrease the QoS implementation footprint but it does also mean you have to be attuned to new congestion pain points arising where you didn't implement QoS. (BTW typical network monitoring, e.g. 5 minute SNMP bandwidth utilization polls, often don't show the need for QoS. However, any port drops or deep queues can be a clue to a congestion issue.)
