That has not been my experience. I'll just use the example of surgical dermatology as that is primarily what I practice now but I can generate any number of examples across all areas of dermatology residency training.
I did my residency at the "lower tier" program in town. That being said, our program had a strong focus on churning out private practice dermatologists and in particular, efficient private practice dermatologists. We had more than adequate volume within any area of dermatology and in particular surgery. (I tell students all the time that a VA rotation where you get to be the primary surgeon is always a huge plus) I graduated and had very few issues making the transition to private practice.
The other residency program in town is a very well-known perennial "top 10" program. Yes, I'm sure they meet the ACGME minimums for surgical volume. However, having done an away rotation at their program as a PGY4 amongst their PGY4s, I can unequivocally state their surgical skills / knowledge were severely lacking and would have put them at a significant disadvantage for an immediate and smooth transition into private practice. (I'm talking basic questions like "how do you place a vertical mattress suture" being asked by their PGY4s, including one who actually was in the midst of applying for a Mohs fellowship)
I went on to pursue fellowship training a few years later and was able to interact with 2 other residency programs in a different part of the country (1 DO program, another very well known perennial top 10 program, both of whom sent residents to shadow my fellowship program). I also found significant differences amongst them (this was at a time when DO programs did not fall under the ACGME umbrella so perhaps things are better standardized now)
tl ; dr = if you are desperate, then yes, pick any program you can get into and take it from there. If you have the luxury of selecting, pick the program that you think will provide the best training and don't let small items like "I'll miss out on 1 year's salary" cloud your judgement