Parshat Shelach begins:
I do not believe that these two accounts are contradictory, for two reasons.
Firstly, there is a big dispute among scholars whether codes such as the Code of Hammurabi or the law codes in the Torah were written as law codes or as case law.
The difference between the two: as a law code, legislators sat down and wrote a comprehensive, theoretical law code to cover various cases. as case law, a case came before a judge, he decided it, the details such as the names of the litigants were stripped away and it was generalized, and written down to cover that situation and situations like it.
Thus, is ki yinatzu anashim yachdav the result of two men fighting and the wife of one intervening, or did this start out entirely conceptual. Sometimes, specific details in the code suggest it is case law. On the other hand, comprehensiveness and specific writing style suggests law code.
Most often in Torah, the case behind the situation is not given. Yet we see in parshat Yitro that people were coming day and night to Moshe to ask him questions, for many of which he made inquiry of Hashem. And we do have occasion where we see the incident beforehand. Thus, the blasphemer, the chopper of wood, and the daughters of Tzelofchad. This is not necessarily the comprehensive list, but rather just thoise instances when the Torah recorded the query besides the final law.
Indeed, one can frame this as the question whether the Torah was given megillah megillah - scroll by scroll throughout the period in the wilderness, in a gradual revelation to Moshe -- or all at once on Har Sinai.
If so, when the people suggested that Moshe send spies, Moshe, though thinking it a good idea, would have consulted God. And this is the subject matter of parshat Shelach.
Secondly, we must realize that parshat Devarim, and much of Devarim, is polemical. Moshe is giving mussar to the Israelites. This is not a history lesson but a focus on failings such that they can improve their actions in the future. True, details are different from that in Shelach, but that is because Moshe omits some details and expands upon others for polemic effect. (Kind of like the author of Afikei Mayim...)
Thus, Moshe focuses on the fact that it was the people's initial suggestion without mentioning Hashem's approval of the plan. He mentions that the spies (all of them) said that the land was good and then focused on the people's reactions, and does not focus on the negative aspect of the spies' report. This is not a conflict between two sources/accounts of the same event, but rather the result of a speaker with an agenda picking and choosing those details to stress for maximum effect.
I believe that these two reasons work together to eliminate any apparent contradiction.