That was certainly part of it, but you have to remember that the far bigger concern at the time was the plague. Justinian's campaigns to conquer Italy failed not because of backdoor maneuvering or failure to reinforce his generals as much as he ought to have; the campaign was essentially won in 540, and by Belisarios at that. (Though his methods had to be somewhat suspicious to Justinian. Pretending to accept the Ostrogoths' nomination as Roman Emperor, then using it as a pretext to have them all killed at the celebratory banquet after he and his troops were let into the city? Hell, I can understand why Justinian would've been stingy with reinforcements after that...only a few decades before, both eastern and western Empires, as you heard in the podcast on Zenon, were wracked with near-constant military intrigue. It was very well within the realm of possibility for Belisarios or whomever to just take his army and march off to try to become emperor. Trust issues were not entirely unrealistic, even if they were a factor, and I don't think that that was the main problem.) And then the plague, the famous 'Justinian's Flea', hit, and the empire suddenly saw its tax base slashed by as much as a third, its manpower disastrously depleted; to boot, the Monophysites, reenergized by Baradaios' mission, were making trouble again, and the Sasanians were attacking in the East. Under the circumstances, I think Justinian, or even the Byzantines in general (insofar as anyone should really place blame on an entire society for much of anything), can't be faulted for the long-term effects of the Gothic Wars. After 540, they had to be downgraded in priority no matter what. Belisarios got the gooey end of the stick there because he was the best general they had, so if you want to keep as much of Italy as you can with virtually no resources, you might as well assign one of the most transcendant military officers in history there - even if the whole thing will be an intensely frustrating experience for the officer in question, and prevent him from taking his place next to Alexander or whomever on masturbatory military historians' lists of Greatest Generals in History a millennium in the future.
Eh. It also had more than a millennium-long run. Not too shabby for a state that tends to go down in history as an internally divided wreck, full of intrigue and plotting and coups. I'm sure that for every crucial flaw in the Byzantine state and society (again, insofar as a society can have a 'flaw') there was a matching advantage that helped sustain its longevity further than most states of Antiquity.