Diagnostic technician claims "no problem"

2001 Chevy Venture: I just purchased from friends, was told don’t drive over 35 mph due to transmission won’t go into high gear. The transmission was recently professionally flushed by them a month ago. We took it to a new mechanic to check the sensors with his computer system, he did and drove it at 70 mph and claimed, “runs good–no problem!” I read the article on Limp Mode and the difference between flushed or changed transmission fluid and am worried we could cause more damage. Tow charges in my rural area are too expensive to leave to chance. Please advise.