Whether or not Rav Elyashiv shlita penned that statement, the issue – and there is an issue – is NOT one of everyone having to be in kollel.
The issue is whether or not it is a good idea to send an 18 year-old bochur into the Nachal Chareidi or not.
It is true that the Nachal Chareidi is overwhelmingly not chareidi. And the recent specter of soldiers being penalized for walking out rather than hearing kol isha – these were top soldiers in officer training, and they were dismissed – gives tremendous weight to what is and has always been one of the main obstacles to sending boys to the army: That there is an anti-religious agenda there.
If Rav Elyashiv did write this letter, please note that there was no reference to married men making a living, to any of the myriad vocational training programs that are available to chareidi men and women, or even to married men going to the army, as many who already have 3 or 4 children do.