Well if it's from the same individual, then I guess that throws out the possibility of a homozygous SNP, unless there's some technical artifact in de novo alignment that could lead to that (I know very little about de novo alignment beyond the absolute theoretical basics, so i can't say!).

But perhaps it's the terminology that's causing the problem here. The term "SNP" is very ambiguous, and some people will swear blind that it means X, while another chap is sure it means Y. Often X will be a senior tenured geneticist and will argue from authority, whilst Y will point to a text book or Wikipedia and argue from a different kind of authority. Truthfully, the term was coined before anyone really knew what was going on, and it doesn't hold a whole lot of value since it's so ambiguous.

Every base in your genome with a 1:1 mapping to a reference genome has the probability of being one of 4 states - A,C,G, and T. The reference base is usually the most commonly seen base in the population - but not always, as there are some human SNPs which occur above 50% frequency. In fact, the very idea of a reference genome doesn't really make much sense if it's just down to frequency - when the UK10K was first being established, I sat in some very long and boring conference calls where we discussed what we should do to prevent UK SNPs from dominating dbSNP and artificially inflating the allele calls, which might lead to the reference human genome becoming very UK-centric, which would obviously unfairly effect the mapping rates of DNA from less-established countries. (NB: This was 5-6 years ago before long NGS reads where a thing, in fact people thought they'd get smaller and more numerous).

So to some, a SNP is a single base variation compared to the reference which occurs with a significant frequency, like above 1%. To others, just 1 occurrence is enough to be called a SNP (although I would call that a variant, not a SNP). Others still will drop the "single base" qualifier and say it must be a "single unit", such as a multi-base deletion or even multiple bases that change together such as CTG to CAG (both code for Serine, so this is actually pretty common). Other's would call that two SNPs. Bioinformaticians often say SNPs are single-base whilst multi-base insertions and deletions are something totally different called "indels" -- however that is a fairly recent distinction created as a result of the software that returns these variations producing one file for the single-base variants, and another INDEL file for the insertion/deletion variants. An old-school geneticist might say such distinctions are meaningless, however they probably don't appreciate that two individuals could have the exact same genome, but their VCF files have different indels.

So depending on your definition, you can have a homozygous SNP having sequenced just 2 individuals from the entire species - however it might not be a SNP for long, after a 3rd individual gets sequenced. You see the issue.

Even if the trace archive had other individuals on it, wouldn't you get conflicting information if you input all of these reads (from Clint and some other individuals), so it wouldn't call a SNP?

So maybe in light of the above, this is a little clearer to you now. There's no such thing as conflicting information. There is only good sequencing and bad sequencing :)

EDIT: Oh and for a simple SNP caller you probably just want samtools mpileup or something, and parse the output for at least three reads that support the SNP and forget probabilities all together. You're not really calling SNPs - you're excluding regions that may be SNPs, but keeping all the sequencing errors. Essentially, you are trying to find (to exclude) regions where 100s of reads all start from an indel (like this: Strange Pattern in Bam File ) because that has a legitimate chance of b0rking the BQSR.