Reproduction steps:
1. Open project attached (SpriteMeshBreaksWhenPacked.zip)
2. Open scene Main
3. Press play.

Expected result: All three sprites will look identically or very similar to each other.
Actual result: Sprite in the middle changed its appearance.

Workaround: In advanced settings set Alpha Source to "Input Texture Alpha" and mark Read/Write Enabled.

Notes: This problem only happens when texture import settings has packing tag set to "[TIGHT]" and compression set to "High Quality".
That sprite is also affected in Sprite packer.
Problem does not appear when using "High Quality" compression with "[TIGHT]" or when using compression "[TIGHT]" but other compression type.

Reproduced on: 5.5.0f3, 5.5.0p4, 5.6.0b4.