Is this true of all training and endorsements? If I lose my logbook am I not a PPL?
First, your logbook doesn't show you are a Private Pilot -- your certificate does, and even if you lose that, the FAA will send you a replacement. However, you asked about training and endorsements, and the FAA guidance on lost logbooks is as follows:
5-321LOST LOGBOOKS OR FLIGHT RECORDS. Aeronautical experience requirements must be shown for a person to be eligible for the issuance or to exercise the privileges of a pilot certificate. A pilot who has lost logbooks or flight time records should be reminded that any fraudulent or intentional false statements concerning aeronautical experience are a basis for suspension or revocation of any certificate or rating held. The pilot who has this problem may, at the discretion of the ASI accepting the application for a pilot certificate or rating, use a signed and notarized statement of previous flight time as the basis for starting a new flight time record. Such a statement should be substantiated by all available evidence, such as aircraft logbooks, receipts for aircraft rentals, and statements of flight operators.
In addition, previous 8710-1's are considered acceptable for proving the flight time entered on that form, since the examiner should have validated that information against your logbook at the time of the practical test. Notice, however, that this only covers flight and training time, not endorsements.
As I see it, unless the flight time you can document covers the endorsement in question (e.g., documented tailwheel PIC time prior to 4/15/91 grandfathering you for 61.31(i)), you will need to get any endorsements you need re-entered and signed by the instructor who gave them. Obviously, if the instructor involved is available and has the records necessary to put a new endorsement in your logbook based on the training previously given, that's easy. Otherwise, you'll need to find another instructor who can give you the necessary training and endorsement.
My guess is that this will be a problem primarily for 61.31 additional training endorsements, flight review, and IPC's. Endorsements for certificate and rating training should be much easier to reproduce since it's more likely the instructor who gave you the original endorsement will still be available and have the records.
And, as stated above, having a photocopy of your logbook pretty much makes all this go away (including the endorsements of which you have copies) once you attach a signed and notarized statement that it's a "true copy" of the lost original.