I don't think the documentation is wrong at all. There may be something wrong with DBD::mysql in your case and perhaps with DBD::Oracle in the past but for DBD::ODBC and DBD::Oracle now

perl -le 'use strict; use warnings;use DBI; my $h = DBI->connect("dbi:
+ODBC:does_not_exist", undef, undef, {PrintError => 0, RaiseError => 0
+}) or die $DBI::errstr;'
[unixODBC][Driver Manager]Data source name not found, and no default d
+river specified (SQL-IM002) at -e line 1.

[download]
perl -le 'use strict; use warnings; use DBI; my $h = DBI->connect("dbi
+:Oracle:host=fred.example.com;sid=fred", "xxx","yyy", {RaiseError => 
+0, PrintError => 0}) or die $DBI::errstr;'
ORA-24327: need explicit attach before authenticating a user (DBD ERRO
+R: OCISessionBegin) at -e line 1.

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they both seem to work fine for me. Interestingly, every time (except for the OP in this thread) I see this mentioned these days it is DBD::mysql. However, for me even DBD::mysql works fine: 
perl -le 'use strict; use warnings; use DBI; my $h = DBI->connect("dbi
+:mysql:database=testd", "xxx","yyy", {RaiseError => 0, PrintError => 
+0}) or die $DBI::errstr;'
Unknown database 'testd' at -e line 1.

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I'm using all the latest released DBDs and DBI.

In reply to Re^3: $DBI::errstr is always undef by mje
in thread $DBI::errstr is always undef by spivey3587

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