The "signed on date" field of any signature message format is only trustworthy if you trust the signer to not
- modify the software to include an arbitrary date (or use a software which allows setting the date) or
- change his computer's system date.
So, if the signer wants to use this field to prove that this was signed at some time (specially, before some time), it is not trustworthy at all.
There are cryptographic means to certify that some data was signed at a certain point in time, but these use either a trusted third party (a signature service, which signs some digest of your message/signed message/... and a time stamp), or even a distributed system with a public time line.
An example would be something like the BitCoin block chain - for every piece of data referred from a block in the chain (i.e. from a transaction) you can be quite certain that it existed before the block was created, as long as the used hash functions are not broken. On the other hand, if you include in your signed data a hash of the latest block, your data bundle is certified to be newer than this block. (But of course, you could have recreated it later.)