This principle is correct and is founded on an authentic Hadeeth:
إذا قدم العشاء فابدؤوا به قبل أن تصلوا صلاة المغرب
"If dinner is served, then begin with it before you pray the Maghrib prayer." (Al-Bukhari no. 672 and Muslim no. 557)
When dinner is served, one obviously desires to eat, and were he to pray before eating that meal, his mind would be occupied in his abandoned meal, a state of mind that takes away from humility and concentration during prayer. For this reason the Prophet (sallAllaahu `alayhi wa sallam), said,
"There is no prayer when food is served, and there is no prayer when one is fighting off the two impurities (i.e., when one has to urinate or defecate)."
But it is necessary to mention here that one should avoid the habit of always having dinner at the time for prayer, because this will result in not praying in congregation.