It's hard to understand your post, but in the case of a Single Processor CPU (SP for short) in a Dual Processor board (DP for short), No. It's not possible at all.
The reason has to do with the chipsets, which are not the same between SP and DP systems (very similar, but not identical). Specifically, the X58 has a single QPI channel (chipset for the SP machines), while the 5520 (not to be confused with the E5520 CPU), has 2 QPI channels. Unfortunately, the 5520 chipset is unable to turn off an unused QPI channel, which is why the SP CPU's will not work in DP boards (hardware limitation in the chipset, not firmware).
The DP CPU's on the other hand, can turn off an unused QPI channel, so they can be used in a Single Processor board & X58 chipset (DP CPU's have 2x QPI channels; one to communicate with the other CPU, and the second to communicate with the 5520 chipset). In an SP board however, one is used to communicate with the X58, and the other is Disabled (turned OFF, as it has the additional circuitry needed to do so). But it's not exactly cost effective, as DP versions (same clock and core count) are more expensive.
If you look closely, the first link are upgrades for DP systems ONLY. The second link are the available CPU upgrades they offer on the SP systems.
There's no "magic" here at all. They use 55xx and 56xx parts as upgrades in the DP models, while they offer 35xx and 36xx parts as CPU upgrades for the SP systems. Which are due to the 5520 chipset limitations I've tried to explain.