Your feeling that “this is wrong” is correct. See the man page:
ServerAliveCountMax
Sets the number of server alive messages (see below) which may be
sent without ssh(1) receiving any messages back from the server.
If this threshold is reached while server alive messages are
being sent, ssh will disconnect from the server, terminating the
session. It is important to note that the use of server alive
messages is very different from TCPKeepAlive (below). The server
alive messages are sent through the encrypted channel and there‐
fore will not be spoofable. The TCP keepalive option enabled by
TCPKeepAlive is spoofable. The server alive mechanism is valu‐
able when the client or server depend on knowing when a connec‐
tion has become inactive.
The default value is 3. If, for example, ServerAliveInterval
(see below) is set to 15 and ServerAliveCountMax is left at the
default, if the server becomes unresponsive, ssh will disconnect
after approximately 45 seconds. This option applies to protocol
version 2 only.
ServerAliveInterval
Sets a timeout interval in seconds after which if no data has
been received from the server, ssh(1) will send a message through
the encrypted channel to request a response from the server. The
default is 0, indicating that these messages will not be sent to
the server. This option applies to protocol version 2 only.