Good point, but why not 139 bytes or 141 bytes?

Many years ago I worked on an SMSC. SMS are sent over the same data channels as phone signalling (call setup etc.) using SS7 protocol stack. The SS7 protocol physical layers used fixed size data packets of around 256 bytes, for example on T1 data channels. On top of that you need routing info such as addressing in MTP, TCAP to get the packet to the correct mobile switching center. Then GSM or IS-41 MAP to route to the device. Finally the sms bearer encoding needs some extra bytes for thing like delivery reports and source phone number. This left 160 bytes free.

In other words, SMS messages could be delivered across the communication channel that the devices were already doing in-order to remain in-contact with towers, essentially allowing providers to charge (SMS used to be an add-on) for something that cost carriers basically nothing in transmission costs.

Is that a correct translation?

Yup, exactly.