Plants that come up from roots are more robust than tiny seedlings.

Did you spread the bare roots during planting and how long was the longest root? Is this potential spreading at a distance through soft, fertile soil (possible) or through compacted via foot traffic soil (more unlikely)?

I did spread them, with the longest being maybe 18 inches or so. The soil is mostly clay/sand. It's not very loose I don't think, but there is no foot traffic there.

The one that was 6 or 8 inches wasn't surprise. The one 4 feet away was a big surprise, if it's a raspberry plant. Sure looks like it though.

How about a picture of the distant plant? 4 feet is indeed a long way for a newly planted raspberry to produce an offset.

Here's some pics:

First, the original plant. It is growing one cane from the roots, and a few others from the bare cane that was attached to the roots at planting:

This is the baby plant that is 4 feet away. There's actually 3 or 4 of them, but these are the biggest two:

Here's another raspberry at the end of the row, that is growing a baby 6 or 8 inches away:

And, here's a wild blackberry nearby:

I be dammed, the first photo looks like a blackberry to me. In fact the only one who looks like raspberry is the third picture. What variety were they suppose to be ?

You're more correct than I am. I went out and checked the tags again, and:

pic 1 - Ouachita Blackberry

pic 2 - unknown, about 4 feet from #1. If it's a wild blackberry, I need to get rid of it

pic 3 - Cascade Delight raspberry

pic 4 - wild blackberry