Nah, not really so, "given you a number, you can trust their genealogy." A few years back, The Great Purge
reexamined approved applications and some were found to not be worthy of approval by today's standards. E.g., Matthew Fuller as a Edward or Samuel Fuller descendant. And sometimes, already approved lines are closed for application because the References on old approved applications are not to today's standards.
It's best, and easy, to submit a GSMD Mayflower Lineage Match, for $75. You will be informed of which individuals are not already approved and you will know which generations you must work on.