This is only preview. If you not have problems in exported PDF - never mind. Preview always is not equal to original.
When you say "Alpha Channel, I assume you mean that you chose Object > Clipping Path > Alpha Channel; and that your image actually includes an alpha channel.
With InDesign's support for native Photoshop transparency, there is no need to set a "Clipping Path" at all, so without having done extensive experimenting in this area, I'd theorize the method you used approximates a path based on the alpha channel, rather than producing a direct-render actually showing the "alpha". I suspect this "detection-based approximation" is the reason for your discrepancy.
You'd be better off just Placing the .psd with a transparent background. A non-destructive way to do that would be (in Photoshop) using the "alpha channel" to make a selection, then apply a Layer Mask based on the selection.
PLUS, GeorgeS' point above is a good one. The image you see in the InDesign editing environment is not your image. It is a JPEG proxy image generated by InDesign, and should not be the basis for judgements of quality.
Well, as your screen shot demonstrates quite well, InDesign's Clipping Path feature will produce and apply a clipping path based on an alpha channel in the image, approximating its (the path's) location based on the black/white edges in the channel, factored by the threshold and tolerance settings imposed by the user. This makes it adjustable, movable, variable, approximated, potentially inexact.
As I already mentioned, there is really no need to use this, or any, path feature at all. Just mask, hide, or delete unwanted background in Photoshop; leaving the area transparent, then save as .psd, and Place in InDesign.
Are you sure the Photoshop version that you showed us is the same file you placed in InDesign?
The reason I asked is; look at the gray end plate, in your Photoshop doc the upper end of this part appears to be thin as paper.
Both of the images in Indesign have this upper part as having the same width as the lower part.
Indesign will create a perfect PDF output based on your Photoshop transparency. No need to add a path either in Indesign or Photoshop.
If however the layer mask as shown is not perfect, rework it in Photoshop.