I find that if the pressure is not to light, nor too strong (Goldilocks...) I can handle massage. It requires developing trust and confidence in someone though. I have two. One is a chiropractor that moonlights. The second, has 20 years experience, and has a background of teaching massage.

Self-massage after a block might be enough to do help, though...

Alt-I read the link to mean that massage was needed to remove certain substances from the injury site, so that it is actually a chemical reaction that's most important, not a matter of desensitization.