Sam flags for bwa-aligned paired end reads with identical + / - strand coordinates

[spark]

I'm looking at some paired end WGS data from a library with very small insert sizes, meaning that many of the DNA fragments are sequenced fully in both directions.

Reads were aligned to a template genome using BWA. For many reads, the insert size is zero (i.e. forward and reverse strand coordinates are identical) These reads are being flagged by bwa sampe as improperly paired (sam flags 81 & 161 or 97 & 145), whereas I think they should count as properly paired.

My question is whether downstream tools (specifically GATK realignment and SNP calling) will exclude these reads, and if so what I would need to do to get round the problem. (One workaround solution would be to extract these improperly paired reads, trim an extra base from the 3' end, then realign.)

As an example:
HWUSI-EAS174:5:102:602:453#0 97 chr1 66904 15 22M = 66904 22 CCAGGAGGCAGCAGCAGTAGCC B@?AA=A@@=A><>=A94>==9
HWUSI-EAS174:5:102:602:453#0 145 chr1 66904 15 22M = 66904 -22 CCAGGAGGCAGCAGCAGTAGCC B=6B4@A?69@9<B?;7=BABA


Thanks,

Stephen