The real lie is in the assumption that the Japanese language is genetically related to Chinese. There is long cultural contact, and heavy lexical/morphological borrowing, but the underlying structures of the two languages remain distinct.
To answer your question, we need to first define tense and aspect.
Tense is a morphological change in verbs to denote when an event took place (past, present, future).
Aspect is the addition of morphological elements to denote the manner in which an event took place (to completion, on-going, etc.).
Japanese verbs most certainly have a past tense. It cannot be related to the Chinese 了, because 了 cannot be applied universally to all verbs, whereas every Japanese verb has a ~た form.
J: する → した、行く → 行った、頼む → 頼んだ
E: have → had, play → played, pay → paid, drink → drank
Now, consider the following set of sentences (parentheses denote comments):
(1) "I was Thomas" (but not anymore)
(1Ca) *我是了Thomas 'I was Thomas' (ungrammatical)
(1Cb) ?我是Thomas了 'I am already Thomas' (non-past)
(1J) 私がThomasでした。 'I was Thomas'
1Cb fails to show that the event is in the past; and 1Ca illustrates an even more important issue -- the aspective 了 doesn't have to attach to the verb. In order to achieve the preterite sense of 'be' in Chinese, you have to insert a time adverb like 以前 (我以前是Thomas)。
Preterite (simple past tense) た can't exist on its own, like English preterite -ed can't. It's an internal change to the verb form itself that makes the important distinction between tense and aspect. (Hence, technically, English has no future tense, since it employs modal verbs in order to achieve futurity.)
However, you are correct in that the preterite form also tends to subsume a completion interpretation, because of a lack of any other intervening aspects.
'I ate something' (past tense, but also interpreted to mean it's completed)
'I have eaten something' (I tried something, but maybe didn't eat the whole thing)
'I was eating something' (I was in the process of eating -- not finished)