In the Lai et al. 2018 preprint from Didier Stainier's group, Morpholino knockdown of vegfaa showed no stress gene response. This demonstrates that the stress gene upgregulation seen with knockdown of egfl7 and some other transcripts is not a response to the Morpholino backbone but a response to the loss of the target's expression. The Robu et al. 2007 p53 paper showed that if Morpholino knockdown of a transcript caused a p53 response, knockdown of that target with a different oligo type (in their case a modified PNA) caused a similar p53 response, again a response caused by the loss of particular proteins.
(this paragraph added 13 Dec 18) Didier Stainier has a recent preprint describing triggering genetic compensation by fragments form the nonsense-mediated decay pathway. It is possible that it is not the loss of a protein but instead is the product of RNA decay that acts as a trigger for the p53 or stress responses as well, though the preprint describes only the compensation response to RNA fragments. (Genetic compensation is triggered by mutant mRNA degradation. bioRxive. 2018. doi:10.1101/328153)
These studies reveal more about biological responses to a knockdown and the contrast of knockdowns and knockouts. Especially combined with observations of a mutant, the loss of target function in a wild-type organism (an uncompensated background) can reveal more information about the target protein's function and the cellular response to its loss.
As demonstrated by the stress response to the Standard Control oligo at elevated doses, keeping the dose of a Morpholino as low as practicable improves the oligo specificity, decreasing the probability of stress responses.
Lai et al. 2018. https://www.biorxiv.org/content/early/2018/11/27/479188