No. The rate might not be too low. The rate might actual be the correct rate. Just because people aren't willing, or able, to work for that rate, does not mean that it is possibly or the correct decision to increase the labor's wage.
And in my opinion this story is a good example of the markets working properly. Consumers are willing to pay a certain amount for a good. The previous workers have better opportunities, and are deciding to stop working for the lower wage. The producers have accepted this, still want to produce the good, and have instead found other ways to ensure the cost of production meets the ability to sell it at a price that consumers are willing to pay.
1) Not being able to fill jobs at a given pay rate is the *classic* economic sign that the wages offered are too low. One of the farmers in the article said that people were not willing to move to the country to farm. This is further the classic case on non-incentivized labor. That quote says they know exactly what the problem is, the producers just aren't willing to remedy it with higher wages.
Personal commentary: They've been use to paying immigrant labor depressed wages for decades. Maybe they just believe that fruit pickers "shouldn't make that much" and the Mexicans are being uppity.
2) And you know what the consumer price cap for strawberries is? Please inform us, what is the price elasticity co-efficient of produce? And if indeed the farmers were to pay $3 - $5 an hour more for labor, how much exactly would that add to the price-per-unit of the goods?
First slaves, then "family farms", then Mexicans, and now possibly machines. From it's early days in the U.S. farmers have looked for ways to depress labor costs This trend continues today. The article linked to is filled with lazy quasi-economics and farmer fear mongering. One is well served to look outside the industry and it's participants to understand its true economics.