Let me correct my last comment.
1) In scenario 1, grub-probe -v -t fs / shows the message preceding the error is "opening (gptvg-lvroot)"
2) In scenario 2, grub-probe -v -t fs /data shows the message preceding the error is "opening (gptvg-lvdata)"
If I replace -t fs with -t partmap in the commands above, the result is the same. So it seems that for grub-probe discovering the partition map is an interim step to discovering the filesystem type, and that's where the problem is.
Let me correct my last comment.
1) In scenario 1, grub-probe -v -t fs / shows the message preceding the error is "opening (gptvg-lvroot)"
2) In scenario 2, grub-probe -v -t fs /data shows the message preceding the error is "opening (gptvg-lvdata)"
If I replace -t fs with -t partmap in the commands above, the result is the same. So it seems that for grub-probe discovering the partition map is an interim step to discovering the filesystem type, and that's where the problem is.