The questionnaire linked in your question is specifically about visiting family in the UK. Since you will be visiting for work related purposes, that doesn’t apply. The page you’re looking for is this one, which says:
##If you’re visiting for certain business or academic activities
You can come to the UK as a Standard Visitor for up to 6 months without a visa, but you can only do certain business or academic activities, for example go to a conference or a meeting.
- do paid or unpaid work for a UK company or as a self-employed person
- do a work placement or internship
- sell directly to the public or provide goods and services
That’s still a bit vague, and they provide a link to the Immigration Rules Appendix Visitor: Permitted Activities. Under work-related training it says:
PA 10.2. Employees of an overseas company or organisation may receive training from a UK based company or organisation in work practices and techniques which are required for the visitor’s employment overseas and not available in their home country.
Based on your description it’s not clear if the training you intend to follow meets those criteria. Specifically, it’s not clear if the training is not available in your home country. As such, I think the following options is the most logical: Ask the UK parent company whether their training qualifies under PA 10.2 of the UK’s Immigration Rules Appendix Visitor: Permitted Activities, i.e. whether you may attend the training as a visitor to the UK.
Another approach would be to get a work visa just in case. In that case you would need to get it through your employer anyway so they can sponsor your visa. So even when you choose this option the employer (or the UK parent company) seems like the best starting point for your question.
As for the work-related training exception, there’s some guidance in this document by the Home Office (specifically related to the PA 10.2 allowed activity):
Training should be in work practices and techniques that are not available in the
visitor’s home country. It should typically be class-room based or involve
familiarisation or observation. Practical training is however allowed provided it does
not amount to ‘training on the job’ or the person filling a role. It is acceptable for a
visitor to learn how to use a piece of equipment in the UK, but you must carefully
assess how long they intend to do this for and make sure there is no risk that they
will be working for that company in the UK.
Where you think the training is available in their home country, you may want to
question why the visitor needs to come to the UK.
If the visitor states that they will be being trained for longer than one month, you
should consider who will be covering their work overseas and whether their training
activities actually amount to taking employment in the UK.
Based on that, it seems the main criteria are that the activity in the UK doesn’t amount to actual work and the training is not available back in the US. Again, this is something the UK parent company knows because they will most likely have dealt with foreign trainees before.