There's a difference between the term "being published" that gets thrown around quite a bit, and having your own "publication".
If you're listed beyond second author on a pub, should you refer to as "my publication on xxx"? No (unless there are extremely extenuating circumstances). Can you put it on your CV under Publications? Yes.
Anybody in academia (PIs, adcomes, whatever) understands the difference between these two, and all that it entails.
This is exactly correct. 1st author >>> 2nd = 3rd = 4th etc. But those secondary authors are still valuable and contributing their intellectual material, not simply running PCR or washing dishes.
And for an undergrad who is looking to be published in a timely manner, I would suggest looking for a young untenured professor in a biotechnology field. (S)he's less likely to have a great deal of hierarchy in the lab which will prevent you from getting a position where you can make intellectual contributions, and (s)he is less likely to sit on a publication once it's ready to go.