I can offer my experience ~15 years ago, which may be relevant or entirely dated. Brazilian visas were always difficult, but I got mine in Buenos Aires with neither bank statements nor air tickets, explaining that I was traveling by land, where I was going, why, how, when, and probably answering a host of other questions, perhaps with proof (or "proof"). It took patience and persistence.
The other obvious option is for your friend to 1) secure some bank statements, which is not too difficult in this day and internet-connected age, and 2) buy a refundable air ticket, which might be expensive in the short term but a wash in the end.
You might also do a site search on the subject, since Peruvian enforcement has been evolving recently. It's my understanding that people have been having Peruvian friends bring bikes over the border, since unlike foreigners they're allowed to do so.
Hope that's helpful.
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