Yes, the cutoffs used by the major companies and webpages are a good guide, and several places use about 7 cM as their cutoff.
This reference gives some details .
There are two issues in this - false positives and false negatives. The more you eliminate one of these by where the cutoff is set, the more likelihood there is of the other.
False positives:
This table shows that 7 cM matches are 50% likely to be genuine and 50% likely to be by chance, while at 10 cM 90% of matches will be genuine. I am a little surprised at those numbers.
False negatives:
This table shows how likely the three main testing companies are to find (or miss) a match. First and second cousins will almost never be missed, 90% of third cousins will be identified, but only around 50% of fourth cousins and very few 5th cousins will be identified. Of course if they set their criteria lower, they would pick up a greater percentage, but also pick up more false positives. I think they have the balance about right - they try to miss few closer relatives even though this generates a few more false positives.
One answer to this is to have several relatives test. I didn't match using FTDNA or Gedmatch criteria someone who is actually a third cousin, but my cousin and aunt (who were third cousin and second cousin once removed) did match and so conformed the relationship.
