Those other people would generally be wrong.
Chrono Trigger stuck to one form of Time Travel.
A completly linear kind. You could only travel between Lavos' most active times. Furthermore time progressed normally through these times.
1 Day in 2099 AD = 1 day in 1000AD. Time wasn't messed up because of this. There were no alternate realties as no alternate reality forms of them were present in the end... this is how you can tell there was no such problem.
Chrono Trigger wrote itself around those paradoxes and so they never existed for them to be a problem in Chrono Cross.
Traveling through time doesn't suddenly make Schalla a supergoddess, time travel able to work anymore or Lavos being teleported to somewhere for no reason when he was killed.
Furthermore if you would read what i wrote, you would note that even traveling through time would not create half those problems which come from the writers having inconsistant rules of time travel and alternate realties.
