Thanks @i.sudbery !
You are right, the expression data from the different TCGA cancer types have been obtained from Firehose pipelines and merged together to form the pan-Cancer Atlas expression matrix 'EBPlusPlusAdjustPANCAN_IlluminaHiSeq_RNASeqV2.geneExp.tsv'.
Looking at the pipelines used on Firehose ('MapspliceRSEM' here), it seems that RSEM was used for read quantification, then normalised by setting the upper quartile count to 1,000, as you mentionned.
However, when starting from read counts, I still cannot retrieve similar expression values using GetNormalizedMat, along with MedianNorm or QuantileNorm functions from the EBSeq package (manual here).
whether the exp matrix log transformed?