We know Google has general said it does not offer private SEO or Google Search support. All Google Search and SEO requests should be done in a public setting. But that does not mean that Googlers like Gary Illyes, John Mueller or Martin Splitt do not read your requests, they just do not really act on them if they are sent in a private channel.
In short, in the latest Search Off the Record podcast Martin Splitt of Google brought up how should he deal with private emails or DMs, any private channel support method. In short, Google's internal policies does not allow for Googlers to offer private one-on-one support through private channels to specific sites because it would give that site an unfair advantage.
This does not mean Gary, John or Martin do not read your messages. Martin may miss your message and may simply not respond. Gary generally does read all the messages but likely will not follow up unless there is a wider issue. John tries to direct the person asking the question to ask the question in a public channel, like the forums, Twitter or hangouts. But he will generally not respond to the question in a private channel.
They even discussed when the Google Ads team asks for clients. So an Google Ads rep asks the Google Search team questions regarding organic search for their clients. Google's organic team will not respond to those complaints, even if they go up the channel and reach some VPs, they said.
It is an interesting conversation and you can listen to it on this podcast. The topic comes up at the 09:53 mark into the podcast and goes on for about ten minutes:
The biggest recommendation is to go to John's office hours webmaster hangouts to get better one on one support. Because there is John offering direct help but in a public channel.
Forum discussion at Twitter.