Filtering SPAM mail with an acceptable false positive and false negative rate is part of the service.
Unfortunately for you, the e-mail providers' customers (the users receiving the mail) get to decide what is an unacceptably high false positive/negative rate --- and not you. If e-mail recipients get too much SPAM or if they get mail that they want landing in their Spam folder too often, then they will switch. This provides the economic incentive for mail providers to Get Things Right.
Unfortunately, there is so much spam out there that if you are too relaxed with letting marginal e-mails (or e-mails from marginal network neighborhoods through) the false negative rate could result in so much spam in users' inbox that they will get mad, and switch.
However, it can happen that the email provider can be too sensitive, and there can be too high of a false positive rate. For example MIT recently tried relying Microsoft's spam filtering system. Way too much stuff landed in the spam filter, and while you could go to the spam filter and manually mark e-mails as "not spam" and eventually Microsoft's ML algorithms would hopefully figure it out, the false positive rate was too high and the MIT community (especially the ones with the real power, e.g., the professors) rose up with an outcry, and MIT abandoned using Microsoft's Spam filtering service.