This statement is inaccurate, and further, does not apply to Verizon.
The main point is that Verizon had very healthy profits. Its workers were basically seeking to stay in place, not expensive increases; they were fighting cutbacks. Verizon could've easily met the union's demands. In addition, unionized workers today make up only a small portion of Verizon's workforce.
Unlike the distant past, where a strike by telephone workers would disrupt telephone service, today the situation is different. First, the system is so automated that virtually all calls do not require human assistance. Second, as mentioned, much of the workforce wasn't unionized and in those segments service was not affected. (I believe the entire wireless segment, which is a major part of the business, is all non-union and not affected by the strike.)